Dear subscribers to The Exchange,The following podcasts shows are all related to history and might be of interest and also useful for your classes. They are mostly US-centered, so please feel free to send me your suggestions and I can report a more comprehensive list in a couple of months.
Revolutions is a podcast on political revolutions, produced by Mike Duncan. He also produced, and completed, The History of Rome, on the history of the Roman Empire.
Aaron Mahnke produces Lore, "exposes the darker side of history, exploring the creatures, people, and places of our wildest nightmares."
Dan Carlin produces Hardcore history. From his website "Whether it’s history or current events he’s discussing, his passion is contagious, his approach refreshing and his ideas tickle your brain in all the right places. He’ll make you mad too."
Daniele Bolelli produces History on Fire.
Isaac Meyer (@GiantEnemy_Crab) produces a podcast on the History Of Japan
Other interesting show, mostly for European history, is The Rhine.
Jake Barton is the producer and host of Historium, with podcasts about history and interviews with scholars.
Historian Liz Covart (@lizcovart) hosts Ben Franklin's World
Stuff You Missed in History Class has podcast episodes for a variety of topics and time periods, and also live shows.
Check out four seasons of Revisionist History at http://revisionisthistory.com/ This show by Malcolm Gladwell and Pushkin Industries has been on demand since 2016.
Ridiculous History also offers live shows and podcast shows on world history. It is produced by Ben Bowlin and Noel Brown.