Listen Notes is a dedicated podcast search engine. It provides better results than a general search engine.
Listen Notes also incorporates a podcast database and tool called “Listen Later”. It allows you to build your own playlists of podcast episodes. Check out this example playlist. The playlist you create has a RSS feed that can be added to any podcast player apps.
The website also offers Listen Clips — a tool that allow you to cut a segment of any podcast episode.
Listen Alerts that notifies you when a specified keyword is mentioned in new podcasts on the Internet.
There is also a Podcast Search & Directory APIs for developers.