Podcast catchers allow me to list all the shows I want to listen to. Every day or so, it automatically checks each show on the list to see there are any new episodes for me. If it finds any, it downloads them and plays them for me.
Currently, I use Google’s ‘Listen’ app, but that service is about to be closed down with the imminent closure of Google Reader. I need to replace it. I've downloaded a handful of alternative apps, but they all lacked a feature I find essential. I remain a little flabbergasted that any podcast app out there does it any other way.