…aside from so called “Deck building” games? (I dislike them.)
I guess I may get FTL and Into the Breach but I’ve played them a zillion times. Looking for some new experiences.
The recent X-Com games are pretty great if you like that style of game (turn based tactics).
I had fun with Plague, Inc., which is like a reverse Pandemic (the board game). Instead of trying to stop the spread of disease, you’re trying to infect as many people as possible. Rebel, Inc. is a similar follow-up.
The Wingspan adaptation is really good, if you like the board game. It’s not really a deck builder, per se, but more a Euro-style tableau/engine builder.
Root is another great board game adaptation.
If you like tower defense, the Kingdom Rush series is fun if simple. It’s more action than proper strategy, IMO.
Divinity: Original Sin 2 is more of an RPG, but it has very tactical turn-based combat — I prefer its combat system over XCom.
Kingdom: Two Crowns has a pretty different, almost idle-ish, gameplay loop. I found it a bit too slow-paced but some friends loved it. It’s a pretty different kind of gameplay than most others, so it’s at least innovative.
There are also some games I’ve played on PC that were great, but I worry about those on a small iPad… games like Civilization, Company of Heroes, Tropico, etc. I feel like those would just be better on a regular computer with a much bigger screen.
PS: With GeForce Now running in a browser, you can also play many PC strategy games, but most won’t have touch controls, so you’ll have to hook up a mouse or gamepad controller (or use the virtual on-screen controller).
Similar recent-ish thread for android, most of which have Apple variants.
I’ll note I also mentioned Xcom in that that thread, so there’s a second to @Reply’s first suggestion!
I’ll also throw a second at Plague, Inc. I play/played that one myself far more than I should, and it’s pretty easy to pick up and put down, and I should mention it has “fantasy” elements available including mindworms and zombie invasions if you want to have a break from seeing if you can kill humanity the old-fashioned way.
I think it’s useful to narrow down what @RickJay prefers out of a strategy game. Tower, resource gathering, unit production, tactical movement, what have you.
I’ll second that. Excellent games. I still play XCOM2 on a semi-regular basis. Not for everyone but, if you like that style of game they are among the best there are.
- Kingdom Rush (I think they are up to Kingdom Rush 5 now – this is a tower defense game)
- Company of Heroes
Are they just ports of the NEW X-Com games for PC?
I strongly disliked those, despite being a huge, huge fan of the first X-com games (and the current Xenonaut games.) The new X-coms were not tactics games, they were puzzle games. Each level was nearly impossible to win unless you did perfect, specific moves.
As in the ones from a few years ago? Yes.
Hmm, really? I thought each level gave you a lot of options, depending on your squad makeup and skills and equipment. But I was also playing on the easiest difficulty. For me it was mostly just find cover and snipe, find cover and snipe, throw grenade, cover and snipe, and that was pretty much the whole game.
I didn’t play the original X-Com games though, so maybe they’re a drastic departure and I just didn’t know 
The original X-com games also didn’t have pre-determined and designed levels. They were all procedurally generated.
iOS has a good port of Final Fantasy Tactics. That’s a classic of the genre.
A more recent series is Banner Saga. I haven’t played it on iOS, but it should lend itself well to touch controls. They made 3 of them so you could be set for a while.