Plenty of music style, from Zouk, Zouk love, mazurka, buguine, chouval bwa, gwo ka, bele, salsa, merengue, cha cha cha, reggae, ragga, compas, Cadence, also carnival sound....
Some are more authentic music with traditionnal costumes ( ballet de la martinique ) others are more from the past african slaves, some are more modern, mixture of difference carribean sound
Some of well know musician or group :
Chouval Bwa : Dede St Prix
Mazurka, biguine : Gertrude Senin
Zouk : Kassav, Gilles Floro, Zouk Machine, Paulo Albin, Perfecta, Selecta, Malavoi, Les aiglons, Ralph Thamar, Thierry Cham, Francky Vincent, Experience 7, Tanya St Val, Jean Philippe Marthely, Eric Virgal, Fuzion, Taxi Kreol, Kwak, Fanny, JM Harmony, Jean Pierre Zabulon, Jocelyne Beroard, Luc Leandry, Ludo, Patrick St Eloi, Phil Control, Souskay, ....
Compas : Tabou Combo, Shooga Combo, Djetx , Ti Mano, Magnum Band, Coupe Cloue, Skah Shah, ..
Too many too list, just listen to some of them in Youtube to have an idea....