Block People on Facebook Messenger

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When you block someone they will no longer be able to do things such as tag you or see things you post on your Timeline. If you're friends, blocking will also unfriend them.

To block messages from someone:
iPhone and iPad:
Open a conversation with the person you want to block
Tap their name at the top of the conversation
Scroll down and tap Block
Tap next to Block Messages

Android:
Open the conversation with the person you want to block
Tap , scroll down, and then tap Block
Tap Block all messages

• Source: Facebook Basic Guides