The series You plays with multiple literary genres without being neatly defined by any one.
One clear genre that it references is romance. Both the first and second seasons focus on Joe and a woman falling in love (Beck and Love, respectively). We see them meeting, getting to know one another, doing the classic romantic will-they-or-won't-they back and forth, and ultimately getting together and falling in love.
While the series plays with those romantic tropes, it quickly turns much darker and pulls from the genre of horror. There is suspense, like when we wonder (and maybe even worry, since we see things from Joe's perspective) if Joe will get caught when burying a body in the woods. And there is, of course, violence and murder. There are also elements of mystery, as when we follow along with Joe, like a detective, as he discovers hidden parts of Beck and Love's histories.
What makes this show interesting though is that is takes some of the expectations of those literary genres and turns them on their heads. It's not a romance, because Joe is a psychopathic murderer, but it employs many romantic tropes that make us root for the love story. Because Joe is our protagonist, we see things from his perspective, and we are naturally inclined to be sympathetic to him (especially because we see his traumatic childhood and the way he is protective of Paco). However, we can't ignore the awful crimes he commits in the name of love, so the show is intended to make us feel uncomfortable with how much we relate to and root for Joe.