One of the main reason of the arithmetical significance of automorphic representations is that we can, according to Langlands' philosophy (sometimes only conjecturally) associate to them in a precise way Galois representations. In the last three decades, p-adic families of (p-adic) automorphic forms, parametrized by rigid analytic spaces, have been constructed and studied. Those leads in many cases to "p-adic families of Galois representations", the precise definition of which requires the notion of "pseudorepresentation" or "pseudocharacter". In this talk, based on a joint work with Gaetan Chenevier, I will relate our attempt to begin a systematic studies of those families of Galois representations, and of how we can use them to construct non-trivial extensions between Galois representations : after recalling the notion of, and proving some results on "pseudocharacters", I will explain how we can control the "reducibility locus" of p-adic families, and apply our results to family of Galois representations attached to automorphic forms on unitary groups.