On Android devices, SMS messages are stored in a database on the device, with no built-in way to sync them with some online cloud service (compared to the contacts for example, that may be synchronized to your Google Contacts account).
For this reason, it is worthwhile to put a little effort into setting up a backup scheme for SMS messages – which is the goal of this post.
I use the SMS Backup & Restore app, which is free on Google Play store, along with its free network add-on (which is required for the E-mail and Dropbox-upload features).
This post was written using v5.93 of the app.