Recover deleted phone calls or messages

For phone calls once they are gone from Recents they are gone forever, unless you have a backup that contains them that you can restore to the phone. Note that doing this will overwrite everything on the phone, not just your phone calls. However, your carrier has a complete list of your calls. You can view it on your bill or by logging in to your carrier's account management website.

For messages, if you have NOT enabled iCloud message sync (Settings/<your name>/icloud - Messages) they will also be in a backup made before the messages were deleted. However, if iCloud message sync is on you cannot recover deleted messages.

When did you last backup your iPhone?