Where has my Podcast playlist on my iPhone Gone?

Where have my podcasts gone from my playlists on my iPhone??? I used to be able to put my podcasts into a playlist in iTunes, but now they don't seem to go onto a playlist and can only be played via the Podcast app. This is terrible as you can't organize or loop podcasts, and is dangerous whilst driving as you have to look at the phone after every episode is finished.

Is there a way to organize my podcasts?

Delete the Podcasts app, and you'll be able to play them through the Music app again. Some people have had to reboot their devices to get them to show in Music; turn the iPhone off then on again.