Gender-flipped version of the Harem Genre
Do We Have This (under a different name), Do We Need This; Early Development Phase, Needs A Better Description, Needs More Examples; Seen It A Million Times; Up For Grabs Old Title: Otome. Note that: the current working title is currently a redirect for Harem Genre. Otome Genre (possible/likely redirect) Harem Genre is currently in TRS here.
A Reverse Harem occurs when one of the main goals, besides the plot goal, is to develop a romantic relationship between the female lead and one of several male characters. These works are unsurprisingly geared towards a female market. In Japan, this occurs often enough to be called a genre known as Otome, or "Maiden." This occurs most often in games, and slightly less often in Anime and Manga. Reverse Harem generally mirrors the Harem Genre, though typically with the focus on Fanservice shifted to the emotional relationships between the characters. Though that isn't to say that Fanservice doesn't occur, multiple Bishounen and Hunks compete for the female lead's attention, Shirtless Scenes, abound, and there's even a subset of the genre strictly for Boy's love. This is less likely to occur in western works, but that's not to say it doesn't. Literature aimed at young girls, and Fanfiction are two places this is likely to pop up in the west. Check The other wiki for anything I may have missed in my haste.