Fair warning, there just is not a lot of "popular" writing about the Elamites out there (frankly there's not a lot about them in general). This is just to say that these books are going to be fairly academic. I would recommend either, or better yet both, of these:
- The Elamite World edited by Javier Álvarez-Mon, Gian Pietro Basello, and Yasmina Wicks
- A veritable tome of an edited volume covering basically every conceivable angle of Elamite studies from history, to language, to material archaeology across over 4000 years of ancient history. As an edited volume it contains a wide range of specialized perspectives.
- The Archaeology of Elam by Daniel T. Potts, second edition
- As the title suggests this one is more specialized, but not as much you might expect. Naturally archaeology is a focus, but if you're primarily looking for a straightforward narrative history, this is just about as close as you'll get. This is also a book where the edition is important. You want the 2015 second edition. A lot of the theories proposed or discussed in the original 1999 version were disproved or fell out of favor in the intervening years.
With anything from Iranian history, I also recommend Encyclopaedia Iranica, which is a free, online, academic reference work. There is a whole host of relevant articles about individual cities/archaeological sites and related topics, but starting with the articles about Elam are a great starting point.
I'm not a big video person, so I don't have much to offer there, but I can comment on podcasts if you're still looking for something aimed directly at a general audience. I've got two options, and both come with caveats.
- Iranologie: the History of Iran Podcast by Khodadad Rezakhani
- This is an older one that original aspired to cover the whole history of Iran and never made it past Cyrus the Great. That means it does include the entirety of the Elamite period though. Dr. Rezakhani is a Sassanid specialist affilitated with a number of prestigious universities and research organizations who is absolutely qualified to present the information in the podcast. He just wasn't a great podcast host. It's more like a series of recorded university lectures with pretty low production value.
- It's also a kind of unfortunate victim of time. Neither of the books above had been published when Dr. Rezakhani was producing this show, and since he's not an Elamite specialist, he doesn't necessarily present the most up-to-date view of Elamite history today.
- The Oldest Stories by James Beckley (and yours truly)
- The Elamites here are a bit of an odd thing. I'm actually in the middle of producing some episodes about Elam for this podcast but I am not the host. There are four so far, covering up to the Middle Bronze Age, and there are two more in the pipeline covering up to the Late Bronze Age Collapse. The relevant episodes are all labled with "Elam" and recent, so they should be easy to find in that feed.
- The caveat here, is that this is not my podcast, and the Oldest Stories is a product of evolution. I feel comfortable recommending the podcast in general, but the idea of this show changed over time. Originally, it was very disjointed and surface level, and that shows in the early episodes. Over time, it evolved into a longform narrative history of the Ancient Near East, and the quality of the research and historical presentation improved.
- The host is also not an academic, so issues of academic debate, deeper historiography, etc are usually not addressed. This has also become less of an issue over time, but is worth bearing in mind. It is still a good introduction to the events of the Bronze Age, but won't impart an academic understanding of those events.