ReviewGeek: The Best Podcast Apps For Your Smartphone. “While Apple’s Podcasts does a decent job for iPhone owners and there’s always Google Play Music for Android users, the world of podcast apps is so much more diverse than those two old standbys. Here’s a look at some of our favorite apps to supercharge your podcast experience.” I have been using Pocket Casts for ages and I can’t recommend it enough. They don’t know a thing about me and this is not a paid endorsement. I just think they’re grand.