How can you Block Spam Twitter Notifications?

The Notifications timeline offers a simple way to see how others on Twitter are interacting with you. 

From the Notifications timeline, you’ll be able to see which of your Tweets have been liked, the latest Retweets (of your Tweets), Tweets directed to you (replies and mentions), your new List followers, as well as your new account followers.

Mute notifications for particular words and phrases you’d like to avoid seeing in your notifications with muted words. Mute notifications for accounts you'd like to avoid seeing notifications from. This includes muting accounts you follow or don't know. For muted accounts you follow, replies and mentions by the muted account will still appear in your Notifications tab.

Advanced filters allow you to disable notifications from certain types of accounts you’d like to avoid. In addition, if your account receives a lot of sudden attention, Twitter may insert a notification in your Notifications tab inviting you to adjust these filters to give you more control over what you see.