Right-click (or long-press on mobile) any conversation thread and select Mute Notifications. This silences all push notifications and email alerts for that specific thread.
What Muting Does
New messages in the muted thread still arrive in your inbox — they just do not trigger any alerts
The thread still shows an unread badge so you can see new messages when you open the Messages page
The sender is not notified that you muted the conversation
Muting has no effect on read receipts — those are controlled separately in Settings → Messages
Unmuting
Right-click (or long-press) the same conversation and select Unmute Notifications to restore alerts. Muted conversations also display a small muted icon next to the thread name so you can identify them at a glance.
Tip Muting is useful for active group conversations or chatty contacts. If you want to stop seeing the thread entirely, consider archiving it instead.