There are two styles of competitive partner-dancing. American Style and International Style. Within the American and International Styles of competitive dance, there are two sub-divisions:
American Style encompasses "American Rhythm" (Rumba, Cha Cha, Swing, Bolero, Mambo, and Swing), as well as, "American Smooth" (Waltz, Tango, Foxtrot, and Viennese Waltz).
International Style encompasses "International Latin" (Rumba, Cha Cha, Jive, Paso Doble, and Samba), as well as, "International Standard" (Waltz, Tango, Foxtrot, Viennese Waltz, and Quickstep)
And if dancing in a genre of 4 or 5 dances is not your thing, then, you may compete in a single dance category. A "single dance" event means that you may pick and choose one or all, of the dances listed above. Other dances include the Hustle, Peabody, Merengue, Salsa, West Coast Swing, Country, Argentine Tango, and now even the Bachata is being offered in competitions.