Summary: This expository paper outlines the proof of A. Wiles [Ann. Math. (2) 141, 443-551 (1995; Zbl 0823.11029)], with the collaboration of B. Taylor [ibid. 553-572 (1995; Zbl 0823.11030)] of the Shimura-Taniyama-Weil conjecture for semistable elliptic curves. It also illustrates some consequences of this work on Fermat’s last theorem and the Birch and Swinnerton-Dyer conjecture.