Pocket Casts is one of the more attractive mobile podcast managers out there, and it's pretty accessible too. The Android app is easy to use, and with a cloud sync account, you can keep up with shows across numerous devices. Now the team is expanding functionality to the desktop as well. A web version of Pocket Casts is on its way, and it's currently available in a private beta.
You have to get permission to use the beta, but once in, here's what you see.