diff --git a/CHANGELOG.md b/CHANGELOG.md
index c9818244755..847fdee0dd1 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -35,7 +35,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Removed
 
--
+- Removed deprecated `compute_on_step` argument ([#962](https://github.com/PyTorchLightning/metrics/pull/962))
 
 
 -
diff --git a/torchmetrics/classification/accuracy.py b/torchmetrics/classification/accuracy.py
index 6ed0957838d..5af1f0c5787 100644
--- a/torchmetrics/classification/accuracy.py
+++ b/torchmetrics/classification/accuracy.py
@@ -126,12 +126,6 @@ class Accuracy(StatScores):
               ``preds = preds.flatten()`` and same for ``target``). Note that the ``top_k`` parameter
               still applies in both cases, if set.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Raises:
@@ -175,7 +169,6 @@ def __init__(
         top_k: Optional[int] = None,
         multiclass: Optional[bool] = None,
         subset_accuracy: bool = False,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         allowed_average = ["micro", "macro", "weighted", "samples", "none", None]
@@ -190,7 +183,6 @@ def __init__(
             num_classes=num_classes,
             multiclass=multiclass,
             ignore_index=ignore_index,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
 
diff --git a/torchmetrics/classification/auc.py b/torchmetrics/classification/auc.py
index 0490de54e22..fb43bf525f0 100644
--- a/torchmetrics/classification/auc.py
+++ b/torchmetrics/classification/auc.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Dict, List, Optional
+from typing import Any, Dict, List
 
 from torch import Tensor
 
@@ -32,11 +32,6 @@ class AUC(Metric):
         reorder: AUC expects its first input to be sorted. If this is not the case,
             setting this argument to ``True`` will use a stable sorting algorithm to
             sort the input in descending order
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
     """
@@ -47,10 +42,9 @@ class AUC(Metric):
     def __init__(
         self,
         reorder: bool = False,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.reorder = reorder
 
diff --git a/torchmetrics/classification/auroc.py b/torchmetrics/classification/auroc.py
index 1f0ff2438cd..5f8e2ce59c3 100644
--- a/torchmetrics/classification/auroc.py
+++ b/torchmetrics/classification/auroc.py
@@ -63,11 +63,6 @@ class AUROC(Metric):
         max_fpr:
             If not ``None``, calculates standardized partial AUC over the
             range ``[0, max_fpr]``. Should be a float between 0 and 1.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -113,10 +108,9 @@ def __init__(
         pos_label: Optional[int] = None,
         average: Optional[str] = "macro",
         max_fpr: Optional[float] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.num_classes = num_classes
         self.pos_label = pos_label
diff --git a/torchmetrics/classification/avg_precision.py b/torchmetrics/classification/avg_precision.py
index c57f8d0d96f..464d31b3865 100644
--- a/torchmetrics/classification/avg_precision.py
+++ b/torchmetrics/classification/avg_precision.py
@@ -57,12 +57,6 @@ class AveragePrecision(Metric):
             - ``'none'`` or ``None``: Calculate the metric for each class separately, and return
               the metric for every class.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Example (binary case):
@@ -93,10 +87,9 @@ def __init__(
         num_classes: Optional[int] = None,
         pos_label: Optional[int] = None,
         average: Optional[str] = "macro",
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.num_classes = num_classes
         self.pos_label = pos_label
diff --git a/torchmetrics/classification/binned_precision_recall.py b/torchmetrics/classification/binned_precision_recall.py
index 142d548efa9..29dddefea96 100644
--- a/torchmetrics/classification/binned_precision_recall.py
+++ b/torchmetrics/classification/binned_precision_recall.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Dict, List, Optional, Tuple, Union
+from typing import Any, Dict, List, Tuple, Union
 
 import torch
 from torch import Tensor
@@ -61,11 +61,6 @@ class BinnedPrecisionRecallCurve(Metric):
         thresholds: list or tensor with specific thresholds or a number of bins from linear sampling.
             It is used for computation will lead to more detailed curve and accurate estimates,
             but will be slower and consume more memory.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -122,10 +117,9 @@ def __init__(
         self,
         num_classes: int,
         thresholds: Union[int, Tensor, List[float], None] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.num_classes = num_classes
         if isinstance(thresholds, int):
@@ -203,11 +197,6 @@ class BinnedAveragePrecision(BinnedPrecisionRecallCurve):
         thresholds: list or tensor with specific thresholds or a number of bins from linear sampling.
             It is used for computation will lead to more detailed curve and accurate estimates,
             but will be slower and consume more memory
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -258,11 +247,6 @@ class BinnedRecallAtFixedPrecision(BinnedPrecisionRecallCurve):
         thresholds: list or tensor with specific thresholds or a number of bins from linear sampling.
             It is used for computation will lead to more detailed curve and accurate estimates,
             but will be slower and consume more memory
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -295,10 +279,9 @@ def __init__(
         num_classes: int,
         min_precision: float,
         thresholds: Union[int, Tensor, List[float], None] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(num_classes=num_classes, thresholds=thresholds, compute_on_step=compute_on_step, **kwargs)
+        super().__init__(num_classes=num_classes, thresholds=thresholds, **kwargs)
         self.min_precision = min_precision
 
     def compute(self) -> Tuple[Tensor, Tensor]:  # type: ignore
diff --git a/torchmetrics/classification/calibration_error.py b/torchmetrics/classification/calibration_error.py
index 3dd2a54b0ef..a6349ba4cb1 100644
--- a/torchmetrics/classification/calibration_error.py
+++ b/torchmetrics/classification/calibration_error.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Dict, List, Optional
+from typing import Any, Dict, List
 
 import torch
 from torch import Tensor
@@ -52,11 +52,6 @@ class CalibrationError(Metric):
         norm: Norm used to compare empirical and expected probability bins.
             Defaults to "l1", or Expected Calibration Error.
         debias: Applies debiasing term, only implemented for l2 norm. Defaults to True.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
     """
@@ -69,11 +64,10 @@ def __init__(
         self,
         n_bins: int = 15,
         norm: str = "l1",
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ):
 
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         if norm not in self.DISTANCES:
             raise ValueError(f"Norm {norm} is not supported. Please select from l1, l2, or max. ")
diff --git a/torchmetrics/classification/cohen_kappa.py b/torchmetrics/classification/cohen_kappa.py
index 7dcfd8dda3d..2370fb37e20 100644
--- a/torchmetrics/classification/cohen_kappa.py
+++ b/torchmetrics/classification/cohen_kappa.py
@@ -56,12 +56,6 @@ class labels.
             Threshold for transforming probability or logit predictions to binary ``(0,1)`` predictions, in the case
             of binary or multi-label inputs. Default value of ``0.5`` corresponds to input being probabilities.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns ``None`` if this is set to ``False``.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Example:
@@ -82,10 +76,9 @@ def __init__(
         num_classes: int,
         weights: Optional[str] = None,
         threshold: float = 0.5,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
         self.num_classes = num_classes
         self.weights = weights
         self.threshold = threshold
diff --git a/torchmetrics/classification/confusion_matrix.py b/torchmetrics/classification/confusion_matrix.py
index 36c56f0eafe..52fabc344de 100644
--- a/torchmetrics/classification/confusion_matrix.py
+++ b/torchmetrics/classification/confusion_matrix.py
@@ -54,11 +54,6 @@ class ConfusionMatrix(Metric):
             of binary or multi-label inputs. Default value of ``0.5`` corresponds to input being probabilities.
 
         multilabel: determines if data is multilabel or not.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -99,10 +94,9 @@ def __init__(
         normalize: Optional[str] = None,
         threshold: float = 0.5,
         multilabel: bool = False,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
         self.num_classes = num_classes
         self.normalize = normalize
         self.threshold = threshold
diff --git a/torchmetrics/classification/f_beta.py b/torchmetrics/classification/f_beta.py
index 32a98b7d912..4d1b5b799a0 100644
--- a/torchmetrics/classification/f_beta.py
+++ b/torchmetrics/classification/f_beta.py
@@ -102,12 +102,6 @@ class FBetaScore(StatScores):
             :ref:`documentation section <pages/classification:using the multiclass parameter>`
             for a more detailed explanation and examples.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Raises:
@@ -135,7 +129,6 @@ def __init__(
         ignore_index: Optional[int] = None,
         top_k: Optional[int] = None,
         multiclass: Optional[bool] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         self.beta = beta
@@ -151,7 +144,6 @@ def __init__(
             num_classes=num_classes,
             multiclass=multiclass,
             ignore_index=ignore_index,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
 
@@ -237,12 +229,6 @@ class F1Score(FBetaScore):
             :ref:`documentation section <pages/classification:using the multiclass parameter>`
             for a more detailed explanation and examples.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
 
@@ -268,7 +254,6 @@ def __init__(
         ignore_index: Optional[int] = None,
         top_k: Optional[int] = None,
         multiclass: Optional[bool] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         super().__init__(
@@ -280,6 +265,5 @@ def __init__(
             ignore_index=ignore_index,
             top_k=top_k,
             multiclass=multiclass,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
diff --git a/torchmetrics/classification/hamming.py b/torchmetrics/classification/hamming.py
index 999315ab7fe..58c4975a35d 100644
--- a/torchmetrics/classification/hamming.py
+++ b/torchmetrics/classification/hamming.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Dict, Optional
+from typing import Any, Dict
 
 import torch
 from torch import Tensor, tensor
@@ -40,11 +40,6 @@ class HammingDistance(Metric):
         threshold:
             Threshold for transforming probability or logit predictions to binary ``(0,1)`` predictions, in the case
             of binary or multi-label inputs. Default value of ``0.5`` corresponds to input being probabilities.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -69,10 +64,9 @@ class HammingDistance(Metric):
     def __init__(
         self,
         threshold: float = 0.5,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.add_state("correct", default=tensor(0), dist_reduce_fx="sum")
         self.add_state("total", default=tensor(0), dist_reduce_fx="sum")
diff --git a/torchmetrics/classification/hinge.py b/torchmetrics/classification/hinge.py
index d374aaf3af9..53bfd5f7c6f 100644
--- a/torchmetrics/classification/hinge.py
+++ b/torchmetrics/classification/hinge.py
@@ -54,11 +54,6 @@ class HingeLoss(Metric):
             Which approach to use for multi-class inputs (has no effect in the binary case). ``None`` (default),
             ``MulticlassMode.CRAMMER_SINGER`` or ``"crammer-singer"``, uses the Crammer Singer multi-class hinge loss.
             ``MulticlassMode.ONE_VS_ALL`` or ``"one-vs-all"`` computes the hinge loss in a one-vs-all fashion.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -101,10 +96,9 @@ def __init__(
         self,
         squared: bool = False,
         multiclass_mode: Optional[Union[str, MulticlassMode]] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.add_state("measure", default=tensor(0.0), dist_reduce_fx="sum")
         self.add_state("total", default=tensor(0), dist_reduce_fx="sum")
diff --git a/torchmetrics/classification/jaccard.py b/torchmetrics/classification/jaccard.py
index c3a278e64ef..6a9074ab8bf 100644
--- a/torchmetrics/classification/jaccard.py
+++ b/torchmetrics/classification/jaccard.py
@@ -59,12 +59,6 @@ class JaccardIndex(ConfusionMatrix):
             - ``'sum'``: takes the sum
             - ``'none'``: no reduction will be applied
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Example:
@@ -88,7 +82,6 @@ def __init__(
         threshold: float = 0.5,
         multilabel: bool = False,
         reduction: Literal["elementwise_mean", "sum", "none", None] = "elementwise_mean",
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         super().__init__(
@@ -96,7 +89,6 @@ def __init__(
             normalize=None,
             threshold=threshold,
             multilabel=multilabel,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
         self.reduction = reduction
diff --git a/torchmetrics/classification/kl_divergence.py b/torchmetrics/classification/kl_divergence.py
index f04d1da796f..10877b7a2c2 100644
--- a/torchmetrics/classification/kl_divergence.py
+++ b/torchmetrics/classification/kl_divergence.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Dict, Optional
+from typing import Any, Dict
 
 import torch
 from torch import Tensor
@@ -44,12 +44,6 @@ class KLDivergence(Metric):
             - ``'sum'``: Sum score across samples
             - ``'none'`` or ``None``: Returns score per sample
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
 
@@ -81,10 +75,9 @@ def __init__(
         self,
         log_prob: bool = False,
         reduction: Literal["mean", "sum", "none", None] = "mean",
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
         if not isinstance(log_prob, bool):
             raise TypeError(f"Expected argument `log_prob` to be bool but got {log_prob}")
         self.log_prob = log_prob
diff --git a/torchmetrics/classification/matthews_corrcoef.py b/torchmetrics/classification/matthews_corrcoef.py
index 5e36e1d5acc..15b2c4b6c8a 100644
--- a/torchmetrics/classification/matthews_corrcoef.py
+++ b/torchmetrics/classification/matthews_corrcoef.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Dict, Optional
+from typing import Any, Dict
 
 import torch
 from torch import Tensor
@@ -51,11 +51,6 @@ class MatthewsCorrCoef(Metric):
     Args:
         num_classes: Number of classes in the dataset.
         threshold: Threshold value for binary or multi-label probabilites.
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -76,10 +71,9 @@ def __init__(
         self,
         num_classes: int,
         threshold: float = 0.5,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
         self.num_classes = num_classes
         self.threshold = threshold
 
diff --git a/torchmetrics/classification/precision_recall.py b/torchmetrics/classification/precision_recall.py
index 86ce9f88e03..0c2dc9a9c71 100644
--- a/torchmetrics/classification/precision_recall.py
+++ b/torchmetrics/classification/precision_recall.py
@@ -89,12 +89,6 @@ class Precision(StatScores):
             :ref:`documentation section <pages/classification:using the multiclass parameter>`
             for a more detailed explanation and examples.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Raises:
@@ -126,7 +120,6 @@ def __init__(
         ignore_index: Optional[int] = None,
         top_k: Optional[int] = None,
         multiclass: Optional[bool] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         allowed_average = ["micro", "macro", "weighted", "samples", "none", None]
@@ -141,7 +134,6 @@ def __init__(
             num_classes=num_classes,
             multiclass=multiclass,
             ignore_index=ignore_index,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
 
@@ -231,12 +223,6 @@ class Recall(StatScores):
             :ref:`documentation section <pages/classification:using the multiclass parameter>`
             for a more detailed explanation and examples.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Raises:
@@ -268,7 +254,6 @@ def __init__(
         ignore_index: Optional[int] = None,
         top_k: Optional[int] = None,
         multiclass: Optional[bool] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         allowed_average = ["micro", "macro", "weighted", "samples", "none", None]
@@ -283,7 +268,6 @@ def __init__(
             num_classes=num_classes,
             multiclass=multiclass,
             ignore_index=ignore_index,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
 
diff --git a/torchmetrics/classification/precision_recall_curve.py b/torchmetrics/classification/precision_recall_curve.py
index e9dd0c82a85..2ec1b7a9717 100644
--- a/torchmetrics/classification/precision_recall_curve.py
+++ b/torchmetrics/classification/precision_recall_curve.py
@@ -42,11 +42,6 @@ class PrecisionRecallCurve(Metric):
         pos_label: integer determining the positive class. Default is ``None`` which for binary problem is translated
             to 1. For multiclass problems this argument should not be set as we iteratively change it in the range
             ``[0, num_classes-1]``
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -88,10 +83,9 @@ def __init__(
         self,
         num_classes: Optional[int] = None,
         pos_label: Optional[int] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.num_classes = num_classes
         self.pos_label = pos_label
diff --git a/torchmetrics/classification/roc.py b/torchmetrics/classification/roc.py
index fd5e163a7c0..f8fcc4c1da6 100644
--- a/torchmetrics/classification/roc.py
+++ b/torchmetrics/classification/roc.py
@@ -43,11 +43,6 @@ class ROC(Metric):
         pos_label: integer determining the positive class. Default is ``None`` which for binary problem is translated
             to 1. For multiclass problems this argument should not be set as we iteratively change it in the range
             ``[0,num_classes-1]``
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
 
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
@@ -112,10 +107,9 @@ def __init__(
         self,
         num_classes: Optional[int] = None,
         pos_label: Optional[int] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.num_classes = num_classes
         self.pos_label = pos_label
diff --git a/torchmetrics/classification/specificity.py b/torchmetrics/classification/specificity.py
index f2e4dfe80aa..4de7400b2cb 100644
--- a/torchmetrics/classification/specificity.py
+++ b/torchmetrics/classification/specificity.py
@@ -92,12 +92,6 @@ class Specificity(StatScores):
             :ref:`documentation section <pages/classification:using the multiclass parameter>`
             for a more detailed explanation and examples.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Raises:
@@ -128,7 +122,6 @@ def __init__(
         ignore_index: Optional[int] = None,
         top_k: Optional[int] = None,
         multiclass: Optional[bool] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
         allowed_average = ["micro", "macro", "weighted", "samples", "none", None]
@@ -143,7 +136,6 @@ def __init__(
             num_classes=num_classes,
             multiclass=multiclass,
             ignore_index=ignore_index,
-            compute_on_step=compute_on_step,
             **kwargs,
         )
 
diff --git a/torchmetrics/classification/stat_scores.py b/torchmetrics/classification/stat_scores.py
index 272ad104ab5..d9866671089 100644
--- a/torchmetrics/classification/stat_scores.py
+++ b/torchmetrics/classification/stat_scores.py
@@ -83,12 +83,6 @@ class StatScores(Metric):
             :ref:`documentation section <pages/classification:using the multiclass parameter>`
             for a more detailed explanation and examples.
 
-        compute_on_step:
-            Forward only calls ``update()`` and returns None if this is set to False.
-
-            .. deprecated:: v0.8
-                Argument has no use anymore and will be removed v0.9.
-
         kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
 
     Raises:
@@ -132,10 +126,9 @@ def __init__(
         ignore_index: Optional[int] = None,
         mdmc_reduce: Optional[str] = None,
         multiclass: Optional[bool] = None,
-        compute_on_step: Optional[bool] = None,
         **kwargs: Dict[str, Any],
     ) -> None:
-        super().__init__(compute_on_step=compute_on_step, **kwargs)
+        super().__init__(**kwargs)
 
         self.reduce = reduce
         self.mdmc_reduce = mdmc_reduce