The Efimov effect is a special three-body binding mechanism occurring in the universal regime of particles interacting with large scattering lengths. This mechanism allows the existence of an infinite number of bound states related to each other by scale invariance. Originally predicted 40 years ago in the context of nuclear physics, it has been investigated experimentally over the last few years with ultracold gases of atoms. In this talk, I will introduce the basic theory of this effect, and present some of its experimental observations, as well as related developments in few-body theory.