La conjecture de Green generique [d'apres C. Voisin]

This is the text of my lecture (in french) at the Bourbaki Seminar (november 2003) on the proof by Claire Voisin of the Green conjecture for a generic curve. This conjecture predicts the structure of the minimal resolution of the ideal of a canonically embedded curve in terms of the existence of certain special linear systems on the curve.