Why is swipe to delete not working on iOS 7 Mail / Messages?

Swipe to delete has not been removed, but it works differently in iOS 7. Users of Messages and Mail on iOS devices have gotten used to swiping from left to right to delete a message. The gesture has been reversed in iOS 7.

To delete a text or iMessage swipe from right to left over the message, then tap the Delete button.

To delete an email message swipe from right to left over the message, then tap the Trash button. Alternatively you can tap the More button to get other options, such as Reply, Forward, Flag, Mark as Read, Move to Junk and Move Message.

Note: The same right to left swipe to delete works with Recents, Favorites, and Voicemail lists in the Phone application.