How to delete messages on iPhone? - 1

If I block someone's number on my phone (iPhone 5s) will it remove our messages in their phone also? So they'll never see it again?

Nope.

No, if you block them and they send you a message to you, it will just say "delivered" but you won't ever receive the message even after you unblock them.

The other person isn't notified when you block them.

Till I tell you, do install LEO Privacy it is far most the best and most reliable app for security which is available for free in Google Play Store and also it has around 4.3 stars from more than 50 millions downloads. Get it and secure your device.

While you can't delete a iMessages - or SMS/MMS - on someone else's iPhone or iPad, you can delete the record of one on your iPhone or iPad. Maybe it was a joke you regret sending, a friend's PIN number you don't want glanced, or maybe you're a secret agent and it's just the way it is. Whatever the reason, you can easily delete any message at any time.

Launch the Messages app from the Home screen.
Tap on the chat containing the message you want to delete.
Tap and hold the message you want to delete.

Launch Messages-tap on a chat and tap and hold a message.

Tap more from the pop-up menu.
Tap on the circle next to the message you want to delete or tap Delete All if you want to get rid of all of the messages in the chat.
Tap on the delete button (looks like a trash can).