If you are on Verizon, you may be able to get them from your carrier.
If you had bothered to previously set appropriate backup options on your phone, you may find them elsewhere. For example, if you were using Hangouts for your texting, you will find all your message history at gmail.com.
Well, as I said, if you were using Hangouts as your messaging app, then you should find your message history by clicking the Hangouts icon (center) which appears at the bottom-left corner of https://mail.google.com
Beyond that, it really just depends on a lot of settings and the apps you actually use.