Young Adult
A Great and Terrible Beauty is young adult fiction, which we know because it has a sixteen-year-old main character who hangs out with other teenagers, and as such, many of the issues at the center of the book are teen issues. We're talking dating, peer pressure, clothes, the popular clique, and more—classic teenage stuff. Add to the mix the fact that the language and story are pretty easy to follow, and we're definitely dealing with a book that's written with young adult readers in mind.
Fantasy
The supernatural bits are what make this a fantasy novel. There is magic and spirits and another world where anything is possible in this book, and any time that happens, we know we're in fantasy land. When Gemma and her friends go to the realms for the first time, they are amazed at the little things they can do, like turn flowers in to butterflies and turn the trees different colors (22.42), and later on they even realize that they have power to change the paths their lives are taking. It's, to say the least, pretty fantastic stuff.
Historical Fiction
While pretty much everything in this book is made up—which makes sense since it falls under the fantasy umbrella—there are plenty of details included that are true to the time period (1895). The girls all wear corsets and traditional Victorian clothes, and society's rigid expectations for them as women are taken straight from the era. So while this book has pretty much one whole foot in the fantasy genre and another foot in the young adult lit genre, it's got at least a couple of toes hanging out in the historical fiction genre, too.