diff --git a/content/docs/command-reference/remote/add.md b/content/docs/command-reference/remote/add.md
index ff283241d6..e4fe375c9b 100644
--- a/content/docs/command-reference/remote/add.md
+++ b/content/docs/command-reference/remote/add.md
@@ -150,11 +150,16 @@ $ dvc remote add -d myremote azure://mycontainer/path
 $ dvc remote modify myremote account_name 'myuser'
 ```
 
-By default, DVC authenticates using an `account_name` and its
-[default credential](https://docs.aws.amazon.com/cli/latest/userguide/cli-chap-configure.html)
-(if any), which uses certain environment variables or a signed-in Microsoft
-application. To use a custom authentication method, use the parameters described
-in `dvc remote modify`.
+By default, DVC authenticates using an `account_name` and its [default
+credential] (if any), which uses environment variables (e.g. set by `az cli`) or
+a Microsoft application.
+
+[default credential]:
+  https://docs.microsoft.com/en-us/python/api/azure-identity/azure.identity.defaultazurecredential
+
+To use a custom authentication method, use the parameters described in
+`dvc remote modify`. See some
+[examples](#example-some-azure-authentication-methods).
 
 </details>
 
diff --git a/content/docs/command-reference/remote/modify.md b/content/docs/command-reference/remote/modify.md
index b1311fea0d..81eddf57ef 100644
--- a/content/docs/command-reference/remote/modify.md
+++ b/content/docs/command-reference/remote/modify.md
@@ -331,10 +331,11 @@ storage. Whether they're effective depends on each storage platform.
   Note that if the given container name isn't found in your account, DVC will
   attempt to create it.
 
-- `account_name` (required) - storage account name
+- `account_name` - storage account name. Required for every authentication
+  method except `connection_string` (which already includes it).
 
   ```dvc
-  $ dvc remote modify myremote account_name 'myuser'
+  $ dvc remote modify myremote account_name 'myaccount'
   ```
 
 By default, DVC authenticates using an `account_name` and its [default
@@ -368,19 +369,24 @@ $ dvc remote modify --system myremote
 
 </details>
 
+> See some [Azure auth examples](#example-some-azure-authentication-methods).
+
 To use a custom authentication method, use the following parameters (listed in
 order of precedence):
 
-1. `connection_string` is used for authentication if given (all others params
-   are ignored).
-2. If `tenant_id` and `client_id` or `client_secret` are given, Active Directory
-   (AD)
-   [service principal](https://docs.microsoft.com/en-us/azure/active-directory/develop/howto-create-service-principal-portal)
-   auth is performed.
+1. `connection_string` is used for authentication if given (`account_name` is
+   ignored).
+2. If `tenant_id` and `client_id`, `client_secret` are given, Active Directory
+   (AD) [service principal] auth is performed.
 3. DVC will try next to connect with `account_key` or `sas_token` (in this
    order) if either are provided.
 4. If `allow_anonymous_login` is set to `True`, then DVC will try to connect
-   [anonymously](https://docs.microsoft.com/en-us/azure/storage/blobs/anonymous-read-access-configure).
+   [anonymously].
+
+[service principal]:
+  https://docs.microsoft.com/en-us/azure/active-directory/develop/howto-create-service-principal-portal
+[anonymously]:
+  https://docs.microsoft.com/en-us/azure/storage/blobs/anonymous-read-access-configure
 
 > The authentication values below may contain sensitive user info. Therefore,
 > it's safer to use the `--local` flag so they're written to a Git-ignored
@@ -391,34 +397,35 @@ order of precedence):
   (recommended).
 
   ```dvc
-  $ dvc remote modify --local myremote connection_string 'mysecret'
+  $ dvc remote modify --local
+                        myremote connection_string 'mysecret'
   ```
 
 * `tenant_id` - tenant ID for AD _service principal_ authentication (requires
   `client_id` and `client_secret` along with this):
 
   ```dvc
-  $ dvc remote modify --local myremote tenant_id 'directory-id'
+  $ dvc remote modify --local myremote tenant_id 'mytenant'
   ```
 
 * `client_id` - client ID for _service principal_ authentication (when
   `tenant_id` is set):
 
   ```dvc
-  $ dvc remote modify --local myremote client_id 'client-id'
+  $ dvc remote modify --local myremote client_id 'myclient'
   ```
 
 * `client_secret` - client Secret for _service principal_ authentication (when
   `tenant_id` is set):
 
   ```dvc
-  $ dvc remote modify --local myremote client_secret 'client-secret'
+  $ dvc remote modify --local myremote client_secret 'mysecret'
   ```
 
 * `account_key` - storage account key:
 
   ```dvc
-  $ dvc remote modify --local myremote account_key 'mysecret'
+  $ dvc remote modify --local myremote account_key 'mykey'
   ```
 
 * `sas_token` - shared access signature token:
@@ -447,7 +454,7 @@ $ export AZURE_STORAGE_CONNECTION_STRING='mysecret'
 For account name and key/token auth:
 
 ```dvc
-$ export AZURE_STORAGE_ACCOUNT='myuser'
+$ export AZURE_STORAGE_ACCOUNT='myaccount'
 # and
 $ export AZURE_STORAGE_KEY='mysecret'
 # or
@@ -1072,3 +1079,42 @@ profile = myuser
 [core]
 remote = myremote
 ```
+
+## Example: Some Azure authentication methods
+
+Using a default identity (e.g. credentials set by `az cli`):
+
+```dvc
+$ dvc remote add -d myremote azure://mycontainer/object
+$ dvc remote modify myremote account_name 'myaccount'
+$ dvc remote push
+```
+
+> Note that this may require the `Storage Blob Data Contributor` and other roles
+> on the account.
+
+Using a `connection_string`:
+
+```dvc
+$ dvc remote add -d myremote azure://mycontainer/object
+$ dvc remote modify --local myremote connection_string 'mysecret'
+$ dvc remote push
+```
+
+Using `account_key`:
+
+```dvc
+$ dvc remote add -d myremote azure://mycontainer/object
+$ dvc remote modify --local myremote account_name 'myaccount'
+$ dvc remote modify --local myremote account_key 'mysecret'
+$ dvc remote push
+```
+
+Using `sas_token`:
+
+```dvc
+$ dvc remote add -d myremote azure://mycontainer/object
+$ dvc remote modify --local myremote account_name 'myaccount'
+$ dvc remote modify --local myremote sas_token 'mysecret'
+$ dvc remote push
+```