Hello! @12blue Thanks for posting your questions.
If your phone is an Android, you can use the AT&T messages service on your tablet or computer and your text and picture messages will be backed up in the AT&T cloud.
You can visit us online at http://www.att.com/shop/apps/att-messages.html for more information. Android also has apps that are 3rd party that will back up your messages. With an iphone, if the messages are imessages you can have your messages sync to your Mac or other Apple device using your Apple ID. Keep in mind that these options would need to be setup prior to any messages being deleted on the phone.
Thanks!
Charise