We all use Gmail account and it is not only used as an email client, but also to backup all your text messages and call log (incoming, outgoing and missed calls) of your mobile.
Having backup of SMS and call logs is always helpful as it would be useful when we lose our mobile or so. We can have a look at our messages from Gmail when we lost our phone.
Here is the simple to backup all your text messages and call logs from mobile to Gmail account.
You can even schedule the backup.