Let N and l be prime numbers, with l > 5 not dividing N - 1; then the image of the l-adic Galois representation attached to the abelian variety J = J_0(N) is as large as it can possibly be. This was proved last week by Ken Ribet if the square of l does not divide the discriminant of the endomorphism ring of J. I shall discuss the techniques that allow us to drop the latter condition.