I saw Tim Harford’s list of best podcasts. I agree with some, but thought he missed some good ones. I don’t know if these are the best, but they are podcasts that I often listen to while working out or walking the dog.
Podcasts for Anyone Interested in Economics.
Podcasts for Economists. The discussions on these shows tend to be directed more toward an audience of economists.
EconTalk Econ Talk is usually directed toward a broad audience, but some episodes are directed more toward economists.
History Podcasts That I Like
A Podcast That I Do Not Like
Revisionist History (link intentionally omitted). I listened to the episode on country music, which I love. If you are interested in having someone that knows nothing about country music explain to you what they think country music is about you should listen to it.