Infectious diseases have been spreading across vast distances for milenia as a result of the movement of both human and animal hosts. In the past, both types of hosts had limited movement ranges, and one observed travelling waves of infection slowly expanding across space. Nowadays, the movement of humans has considerably accelerated and expanded, so that one observes another kind of spread, which appears less coherent.In this talk, I will discuss the mechanisms that give rise to the spatialization of an infectious disease. I will then present metapopulation models, one of the methods that can be used to describe the spatio-temporal spread of infections between distant locations. I will review some mathematical properties of these models, and will illustrate with a stochastic application in the context of the spread of infections via the global air transportation network.