They do. There's lots of podcasting apps in the store, and you can erase the podcasts app and go back to the old way of playing them with the music app. Biggest downside is that you can't download podcasts on the phone without the podcasts app, so either do it on your computer or download the app, get the podcasts and erase the app. There's a few topics on here on how to do this. Search is your friend.