Unfortunately, podcasts and videos are not available on desktop right now. However, there is an idea for this in the Ideas Exchange board, you can vote for it and it might be implemented in Spotify. You can find this idea on this page.
Have a nice day and keep rocking! 🙂
HuboRock Star 16
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That's pretty frustrating, I just started listening to podcasts, I would like to be able to listen if I'm at my desk as well as on the road. If they are available on the mobile verson, they should be on the desktop version.