How to block/unblock someone on Twitter
Block is a feature that helps users control their interaction with other accounts on Twitter. It helps users restrict specific accounts from contacting, reading their tweets and following them. Blocking someone you are currently following will lead to a cease of tracking that account and vice versa. Blocked accounts will not be notified about the action. However, if a blocked account visits the profile of those who are blocking them, they will see they have been blocked (unlike mute, muted accounts have no way to tell that they are muted, for more details about muting, read this article). After blocking, all interactions with that account, including following, viewing your tweets, sending direct messages, tagging, etc. will be stopped. Follow these steps to block or unblock someone on Twitter.
Note: Blocking only works if the account you’ve blocked is logged in on Twitter. This means that they will still be able to see your public tweets when they aren't logged in. Keep this in mind when you share your content on Twitter, or consider using protected tweets.
How to block someone on Twitter
From a Tweet
Step 1: Click the Down arrow icon at the top of a Tweet from the account you want to block.
Step 2: Select Block @"username".
Step 3: Click Block to confirm your action.
From a profile
Step 1: Go to the profile page of the account you want to block.
Step 2: Click the icon. It's in the bottom right corner of the cover picture.
Step 3: Select Block @"username" from a drop-down menu.
Step 4: Click Block to confirm your action.
How to unblock someone on Twitter
From a profile
Step 1: Go to the blocked account's profile page.
Step 2: Click the Blocked button. It's in the bottom right corner of the cover picture. This button will change to Unblock.
You can go to their profile page and view that person's tweets without unblocking them. This option is not available for the blocked account when they visit your profile.
From your blocked list
You can see your full list of blocked accounts in the Account Settings page.
Step 1: Click on your profile picture in the upper-right corner of the page.
Step 2: Select Settings and privacy from the drop-down menu.
Step 3: Click Blocked Accounts on the left menu.
Step 4: A list of all accounts you've blocked will appear. To unblock an account, click the Blocked button next to the account you want to unblock.