These are the first two volumes of the planned Daevabad Trilogy. City of Brass landed the author on the short list for what is now known as the Astounding Award for Best New Writer (formerly the Campbell Award).
The story is fantasy based on Middle Eastern mythology, history, and religion. Nahri, a young con artist of 18th-century Cairo, Egypt, ekes out a modest living by running various scams, including exorcisms. One night, the seeming nonsense she is chanting to drive a demon from an unfortunate girl has a shockingly real effect: the demon-possessed victim follows Nahri after the ceremony is over and starts to attack her. Out of nowhere, a warrior appears to defend her. Eventually, Nahri and her new protector escape on a flying carpet.
Her protector, nicknamed Dara, calls himself a Daeva, a type of being that we would consider a djinn. Nahri seems to be the descendant of a race of magical healers revered by the djinni, which explains how she can usually heal herself and sometimes other people. Dara insists on bringing her to Daevabad, center of the Daeva world, a mighty city hidden by magic from human eyes and populated not only by Daevas but also by the racially similar but culturally different Djinni.
Perhaps I ought to add that the Daevas are Zoroastrians, while their Djinni fellows are quite devout Muslims.
Daevabad is also, not too surprisingly (I mean, it's clearly that sort of fantasy), a hotbed of evil politics, religious schisms, feuds, and oppression of the shafit, people of mixed human and Daeva blood (like ... Nahri). Nahri soon becomes a fiercely contested pawn, albeit a willful one, in the power games of the city's ruler and his enemies.
The story gains another narrator in Prince Alizayd (Ali), the ruler's younger son, a fiercely loyal and devout warrior who is meant to become the city's military leader. He and Nahri develop a sort-of friendship. And then things start to go very, very badly.
It's pretty much impossible to discuss The Kingdom of Copper without spoilers for the first book, except to say that it is very much not a happy book (although it is a page-turner, like the first one) and ends violently and quite surprisingly.
I enjoyed these but I didn't love them. Some of the themes discussed are quite serious, and I have seen a number of discussions online about whether the author handles them well. I've read that she's a convert to Islam, and some readers don't think she has an "Own Voices" viewpoint on the religious and cultural aspects of the story.
Nahri could easily be Smurfette (TV Tropes link), but Chakraborthy has actually provided a number of female characters to interact with our heroine and with Ali and Dara. None of them are leads/viewpoint characters, but some of them are engaging and all are pretty interesting. Nahri also shows a lot of growth as the story progresses.
Ali has Lots of Issues, and Dara, as has been mentioned elsewhere, is a Hot Mess (and hah, thats somewhat of a bad joke, but I will let it stand).
I certainly intend to read The Empire of Gold, the third volume, which should come out next year.