On desktop: 

On MacOS and Windows, message notifications are managed under System Preferences > Notifications. Select the Wire app on the left, then change your preferences on the right.

On Google Chrome:

When you sign in for the first time, the notification bar will ask you to allow or deny these notifications. Click the lock icon and choose one of the 3 following options:

• ask by default
• always allow on this site
• always block on this site

On Mozilla Firefox: 

You will be asked to choose whether to show notifications for:

• this session
• always show notifications
• always block notifications

On Opera: You will be asked if you want to show desktop notifications.

On mobile devices:

On iOS: Wire message notifications are managed under Settings > Notifications > Wire.

On Android: Wire message notifications are managed under Settings > Apps/App Manager > Wire > Show Notifications.

On Android 8: customize your notifications in Channels: Wire Settings > Options > Text Tone.