Others have mentioned Hardcore History – probably the pinnacle of history podcasting, but the episodes are VERY long (a lot are upwards of 4 hours) and you’re lucky if he puts out more than 2 per year. He does other shorter Addenda episodes that come out more frequently, but they’re not the same format, usually interviews.

History of Rome – it’s older, but it basically started the “History of [nation/civilization]” podcast format. Does an excellent job tracing Roman history from the founding of the city up to the fall of the Western empire in the 5th century.

Revolutions – same host as History of Rome. After he finished HoR he started this one. Each ‘season’ tracks a different historical world revolution (English, American, French, Mexican, Haitian, Russian, and more). Overall, the entire series tracks large-scale western political history from the 17th century up to the early 20th. He ended the podcast after he finished the Russian Revolution. But then he restarted it a couple of years later, running a season on the fictional Martian Revolution of the 24th century. This is on going now, with 6 episodes left. He’s said he’s going back to pick up on historical revolutions after the Russian when he finishes with Mars, teasing Ireland and Iran as future seasons.

Behind the Bastards – Dives into various horrible people from history with a special focus on world dictators/authoritarians, cult leaders, grifters, and quack doctors. He tends to focus on more recent history (past 50-100 years) but sometimes goes into older history.

Cool People Who Did Cool Stuff – An inversion of Behind the Bastards from the same podcast network. Tends to focus on radical political history with a special focus on anarchists, women, and lgbtq people.