There is the BN Mobile app for listening live, and random archived shows when not live. Livestream is good for catching up on the recent shows (since they started using it)
Otherwise, I just download them from the main site, or itunes and drag them onto the device.
I like doggcatcher for the archived shows and other podcasts. It cost $5 when I bought it, not sure if that's changed. For another $5 there's an app that goes with it that will let you speed up the playback. That came in really handy when I got behind on the session.
Nexus 7 - Google Play Music will play the podcasts. BN app is cool too. If you have a Raspberry Pi you can also stream straight to it using the Yatse app, which is pretty cool.