Simulation of large deviation functions using population dynamics

In these notes we present a pedagogical account of the population dynamics methods recently introduced to simulate large deviation functions of dynamical observables in and out of equilibrium. After a brief introduction on large deviation functions and their simulations, we review the method of Giardin`a emph{et al.} for discrete time processes and that of Lecomte emph{et al.} for the continuous time counterpart. Last we explain how these methods can be modified to handle static observables and extract information about intermediate times.