We just shipped Pod − a theme that turns a Ghost site into the actual podcast host, not just a page that links out to one.
In most podcast themes for Ghost the audio and the RSS feed live somewhere else, and the site is just a window onto it. My goal with Pod was to use Ghost’s full functionality to well…not rely on another service.
You upload the MP3 into Ghost’s edit the same way you’d upload an image, write the show notes and publish. The RSS feed comes out of your own domain via Ghost’s routing. The audio file is nicely rendered for anyone listening through your site.
The custom RSS feed is fully compatible with modern podcasting spec: Cast Feed Validator
We’ve been using the technology (and big parts of the theme itself) on our own podcast in the last weeks − and it’s working great 
The theme itself is MIT-licensed and lives on GitHub:
Live demo: https://pod.magicpages.co
Details & documentation: Pod — a podcast theme for Ghost
One neat thing: all configuration for an episode comes from little snippets in a post’s code injection. And we have a generator for that ready here: Episode metadata generator
Let me know what you think! (and I am also curious to see all the podcasts you publish with it!)
