Google introduces Google Podcasts
play.google.com
play.google.com
Google uploads the podcasts and hosts them directly, meaning you must agree to grant Google an irrevocable worldwide license to use your podcast's content, including the ability to present copies of your podcast you have delisted or removed.
This is in stark contrast to iTunes, which treats it's podcast section like an RSS feed, simply facilitating people finding and retrieving your podcast from your servers. Most podcast sites and apps work this way, which is why I'm rarely surprised to find my podcast is listed somewhere new without me even doing anything: People don't need rights to show my RSS feed.
I've had requests to make my podcast available in Google Play, but am holding on Google offering an option that doesn't require rights to my content. And as far as I know, and according to the reviews here on the Play Store, Google still won't let people add their own podcast RSS feeds manually to the app: It requires the podcast have agreed to let Google host it and agreed to their terms.
But at least they let you manage your privacy settings in one place and is somewhat consistent. Cannot really say the same for Amazon for example.