SMS Backup & Restore is described as 'simple Android app that backs up and restores your phone's text messages, and now call logs too!' and is an app in the Backup & Sync category. There are six alternatives to SMS Backup & Restore for Android, F-Droid and Windows Mobile. The best alternative is SMS Backup+, which is both free and Open Source. Other great apps like SMS Backup & Restore are Super Backup & Restore (Freemium), Epistolaire (Free, Open Source), SMS Backup Android (Freemium) and SMS Backup (Free).
Automatically backup your SMS, MMS and call history with a separate label in Gmail and Google Calendar. Later you can restore the saved data (except MMS) back to the phone, especially useful when switching to a new device.
The fastest data backup and restore tool on Android phones! You can backup applications, contacts, text messages, call history, bookmarks, calendars to your SD card, Gmail, or Google Drive You will never lose your data again!.
Epistolaire is an Android app to backup SMSes AND MMSes (unlike most "SMS backup" apps), in a nutshell. - saves SMS/MMSes to a JSON file that's very close to a dump of Android's message database - also saves images etc.
This app will backup and restore sms from your device to an xml file stored in the sdcard/SMSBackup folder. You can choose the filename to save and if you have other backups done choose which backup to restore! Now you can send the backup by email!
This program exports SMS (text messages) to text files * exports any selectable SMS folder * remembers settings * Exports read and/or unread items * optionally only exports old text messages * optional deletion of exported items * Exports to CSV...