Alternate history can be a lot of different types of stories:
You've got purely realistic alternate history, like Harry Turtledove's
How Few Remain. There, one minor thing in history is changed (the Union army does
not intercept a Confederate message), and the book explores the consequences. There's nothing "fantastic" in the story, other than the fact that the book assumes something factual happened differently.
Then you've got historically-based, totally-unrealistic fantasy. An example of this might be Harry Turtledove's (his name will come up a lot with alt. history) Darkness series (which basically shows WWII in a quasi-medieval world with dragons and magic). Guy Gavriel Kay basically writes almost exclusively in this sub-genre: he doesn't write "alternate history" but his secondary (pure fantasy) worlds are heavily informed by real world history.
Somewhere between those first two ends of the spectrum, you've got totally fantastical alternate history that takes place in an "alternate" real world. Imagine our world with magic (Michael A. Stackpole does this with
At the Queen's Command, Patricia C. Wrede does this with her Frontier Magic trilogy, Jonathan Stroud does it with his Bartimaeus books). Theoretically it takes place in "our" world, but there are elements of fantasy that make it completely different.
Then you've got time-travel alternate history, where history is influenced/changed to some extent by people traveling back in time. Mary Gentle's First History quartet is my personal favorite example of this, though lots of people like Connie Willis' books, or Tim Powers'
The Anubis Gates. Another one of my faves is Michael Moorcock's
Behold the Man. Eric Flint does a lot of this, too.
Then you've got "secret history" books. These basically stick pretty closely to actual observed history, but posit events/actors that historians know nothing about influencing major events. One can make the argument that Marie Brennan's Onyx Court series fall into this category: superficially, the history of London is as we know it. But the book's depict a whole complex series of events involving faeries who live in the Onyx Court beneath the city. There's overlap and interaction with the mortal realm, but the "basic events of history" are not changed.
Anywhere between these options you've got lots of other "alternate history" books. Consider just about every steampunk novel out there. They're all alternate history, at some level. Just alternate history of a particular type (check out Gail Carriger, Cherie Priest, Bruce Sterling & William Gibson, etc.).
I'd say alternate history - especially of the steampunk variety - is still going fairly strong today. There's some talk that the steampunk wave may have crested, but there's lots of it in the bookstores. And so much alternate history is published without being called alternate history that I'd venture a guess that it's secretly one of the most popular sub-genres out there.
As someone who loves reading it and writing it, that's what I hope at any rate!
Also, you might want to check out an
essay I wrote earlier this year about techniques in alternate history. Might find some helpful stuff there.
Hope all this helps! Good luck, and good writing!