Currently the only way to catch up on unplayed Podcast episodes is to use the Android App.
On the Desktop the only way to check for new Episodes is to check each Podcast individually instead of having a stream of unplayed Podcast Episodes like in the Android app.
Please include an "unplayed Podcast Episodes" Stream in the Desktop Vesion.
Edit: This idea has been reposted here.
Updated on 2018-10-19
Your idea has been submitted a while ago but unfortunately hasn't gathered enough kudos (100 per year). In order to keep an overview of the active & recent ideas in this forum, we will close this idea for now. However this does not mean that your idea has been declined by Spotify.
If you still feel strongly about your request, we encourage you to post your idea in a little different form again! Maybe now is the right time to receive the support of our community for your suggestion! ;)
P.S: More information about how the ideas exchange works can be found here.