Now that I think of the question...probably more than I realize.
I find their society and political structure fascinating. I always think people from "back in the day" get unfairly judged as not as smart because their technology wasn't "electronic" if you will...but that is not fair or accurate.
To think someone designed and built the colosseum for example like 2,000 years ago is amazing to me.
Not a big podcast person (more of an audiobook guy), but I listened to and really enjoyed Mike Duncan's "History of Rome" podcast. Basically was about 180 episodes, each about 25 minutes and spanned from about 400 BC to 476 AD or there about.
Dan Carlin's Hardcore History did a series about Rome, it's probably like 5 or 6 four-hour podcasts that came out over a couple years. Super awesome, but I'm going to look up this one now.
I agree with you completely about how advanced they were.
This is what gets me about their society, and stays with me from visiting Italy and Rome in particular...it's the raw display of power and wealth of an entity. And when you're traveling around Italy, you're seeing the legacy of two of probably what, five or six most powerful human organization of all time, between the Roman Empire and the late middle age/renaissance Catholic Church.
The sheer scale and amount of what those two entities left behind is staggering when you consider the power and wealth that it signifies to command their creation. There's a lot of "why don't we build wonders any more" rhetoric going around, and the reason is that those things get built as a show of power, and we don't do that anymore.
To see the Roman buildings, and the Catholic Churches, is seeing the residue of a massive execution of power the likes of which the world has only seen a handful of times in the history of mankind, and its all around you. Not one instance here or there to remind you...its everywhere.
There have obviously been a few other societies that leveraged that kind of power, and left remnants of it, from the Great Pyramids to the Great Wall of China, and others. And there were executions of power, like the fast US mobilization for WW2, that didn't leave behind that kind of "stuff".
But to be so surrounded by it just leaves me in awe, because that kind of power doesn't exist in our time, and probably never will again, and its awfully hard to wrap your head around.