If I understand I assume you are in iTunes? In iOS 6 there is an podcasts app that you have to download.
Sorry, I thought that since this is the iPhone 5 forum and I was comparing against an iPod Touch with an older version of the OS that it was clear I was talking about on my iPhone 5 with iOS6.
I'm not interested in downloading a separate app. I'm particularly not interested in having my podcasts download over my phone's data connection. I've got my podcast management setup in iTunes, just like my music management, and it does still transfer them to the iPhone, and they do show up in the music app on the iPhone. But the podcast tab within the music app there seems to go away when there are no podcasts on the device.