In 1994, Wiles and Taylor-Wiles proved that every semistable elliptic curve over $\bf Q$ is modular, in the sense that it is a quotient of the jacobian of some modular curve. This result has since then been generalized by an increasing sequence of groups of authors, culminating in the proof by Breuil, Conrad, Diamond and Taylor that all elliptic curves over $\bf Q$ are modular. Their strategy is essentially that of Wiles, but they have to overcome many technical problems. Especially the deformation theory of local Galois representations becomes much harder.