Born into a family of musicians, Anne Martin studied music at the Lausanne Conservatory (piano with Denise Bidal, a student of Cortot) and dance at the Rosella Hightower International Center in Cannes.

Hired by Gigi Caciuleanu in 1977 at the Grand Théâtre de Nancy, she joined Pina Bausch in Wuppertal in 1978-79, and became a soloist with the Tanztheater from 1979 to 1991. She participated in the creations of Kontakthof, Arien, Keuschheitslegende, 1980-ein Stück von Pina Bausch, Bandoneon, Nelken, Auf dem Gebirge hat man ein Geschrei gehört, Viktor, Ahnen, the film Die Klage der Kaiserin and took over the role of Pina Bausch in Café Müller.

In parallel, she practiced improvisation with the double bassists Peter Kowald and Joëlle Léandre; then she returned to music through singing, street singing and traditional singing, then her own compositions, with the accordion or a capella, and with musicians (Pascal Jaussaud and Jean-Pierre Jullian); she recorded two records, produced by the West Deutsche Rundfunk and then Pro Helvetia.

In 1999, she returned to dance by participating in the creation of Baal (Brecht) and then created a solo dance-voice, Rouge Amande, then participated in the creations of Malou Airaudo, Raimund Hoghe, and Michel Kelemenis; this was followed by a solo, Nafas, with Majid Rahnema, Madjid Khaladj and Pascal Jaussaud.

She then turned to teaching dance. Guest professor at Claremont University and Cal Arts (California), then at the Ménagerie de Verre (Paris), she became a professor at the CNSMD of Lyon from 2003 to 2020.

In parallel, she choreographed for the Theatre and the Opera (Moscou Quartier des Cerises with Macha Makeieff and Jérôme Deschamps, Luci Miei Traditrici with Georges Lavaudant, Orphée for the Berlioz Festival with the Carpe Diem Ensemble).

She became a Feldenkrais practitioner in 2020 and continues to choreograph: two pieces for the Lifting group at the Comédie de Clermont (Pour un Non pour un Oui, 2017, and l'Ombre de l'Eau, 2018,) À Bout de Souffle, 2021 for the BJ of the Toulon Conservatory. Creation in dance-theater for a theater group in Saint-Pierre-et-Miquelon), and revival of Pina Bausch's Auf dem Gebirge hat man ein Geschrei gehört for the Lyon Opera Ballet (June 2022).