The web player works exactly as you'd expect. It shows the podcasts you've subscribed to on the mobile app, what you've listened to, what's in progress, and helps you find new podcasts. All the content is synced with the mobile app, so it's easy to start listening right where you left off. The player itself is a bit bare-bones at the moment, but it works fine even though there aren't many advanced features. The one catch is that the web app costs $US9, but you can get a free 14 day trial to check it out.
Pocket Casts ($US9)