The cavity method is an effective technique born to analyze classical system defined on graphs, and then also quantum systems, at equilibrium; by exploiting graphical models, it is indeed possible to derive self-consistent equations for one-site cavity marginals that, if obtained, allow for the computation of full one-site marginals, so that local observables can be easily computed. At equilibrium, and especially in the case of quantum systems, the results obtained with the cavity method provide a starting point for the application of the dynamical mean-field theory approach: this allows for a description of a many-body problem as a one-body problem by means of a set of effective quantities that have to be computed self-consistently.