In ergodic optimization we try to characterize the structure of orbits of a dynamical system that minimize an observable in the mean. The theory is well developped for Lipschitz observables over a symbolic dynamical system with a finite alphabet. In the Frenkel-Kontorova model we try to characterize the structure of configurations of atoms over a one-dimensional lattice that minimize the total energy. The main difference is that the alphabet is now the set of real numbers. We will try to explain that minimizing orbits in both cases correspond to ground states configurations, that is configurations at the lowest energy level.