In a folder on the phone. I then upload the file to Dropbox. It has a auto feature to do that but you have to download a plugin which I didn't want to do. What I like is it has its own viewer so after I export the texts I can view them even thought they are no longer in the original texting app.
My husband and I text alot. He texts me on breaks and lunchtime and I text him when I need something or just want to share something. So I had all my texts from December 2014 till present on the text app. Now they are backed up and put into a xml file that can be viewed on the backup app's viewer. I look at those texts like a diary between the two of us.
You do want to save all MMS attachments separately. It does not seem to back those up. I saved all photos before I deleted the texts. Hubby will be at the store and see something that he thinks I need to see and sends me a photo of it. Sometimes he will take a pic of a whole display of items then send it to me and ask me to pick one. lol. I love technology!