Given a finitely generated, residually finite group $G$, we ask which properties can be detected from the set of its finite quotients, encoded in its profinite completion. After investigating recent advances in the context of profinite rigidity, we will focus on the interplay between profinite completions and the notion of amenability. We will see, following a construction by S. Kionke and E. Schesler, that amenability is not a profinite invariant by using tools related to automorphisms of rooted trees