Multitytype Galton-Watson processes in random environment (for short, MGWREs) are variants on the well known Galton-Watson process, where the offpsring distribution of an individual of the n-th generation depends both on a notion of type assigned to each individual, and on the value at time n of a stochastic process which represents the environment in which the population evolves. The study of MGWRE is closely related with some products of random matrices or linear operators , depending on whether the set of the possible types of the individuals is finite or not. In this talk, I will present some historical ergodicity results for products of random matrices, as well as an extension of these results to products of infinite dimensional operators. Moreover, I will explain how these ergodicity results allow to characterize the extinction of the associated Galton-Watson process and obtain Kesten-Stigum-type theorems, which yields an asymptotic description of the population when it survives.