Summarize:

Blocking a user on Twitter will prevent them from being able to interact with you on the site.  The person you block will not receive any notification that they’ve been blocked. If the person you block logs out of Twitter and your tweets are not protected, they will be able to view your tweets.  This will expand a menu containing various options. A confirmation window will appear. To unblock the account, return to the user’s profile page and tap the “Blocked” button. You will be prompted to confirm—click “Unblock” again if you want to proceed. Click your profile image at the top of the screen and select “Settings and privacy” Select “Blocked Accounts” from the left menu to view the list. To unblock a user, click “Blocked” next to the user’s Twitter handle.
Sign into your Twitter account. Navigate to the profile of the user you would like to block. Click the ⋮ icon at the top right corner of the user’s profile. Click “Block @Username” in the menu. Click “Block” again to confirm. View a list of every account you have blocked.