I will present a 1976 paper by Ken Ribet called A modular construction of unramified p-extensions of Q(\mu_p), which proves the converse of a classical theorem due to Herbrand. An odd prime p is called irregular if it divides the class number of the cyclotomic field Q(\mu_p). On the other hand, there are so-called Bernoulli numbers which appear as special values of L-functions. Kummer proved that a prime is irregular if and only if it divides certain Bernoulli numbers. The Herbrand-Ribet theorem is a refinement of Kummer's criterion. Ribet's elegant proof weaves together different facets of number theory, including modular forms, Galois representations, and class field theory. We will explain relevant notions in modular forms before focusing on the construction of Galois representations from cusp eigenforms.