Bayesianism is a philosophical approach to science founded on Thomas Bayes’s reasoning about the information contained in causes about effects and in effects about causes. This chapter presents the main concepts related to Bayesian inference and its mathematical foundations from the perspective of the joint probability of (observed) data and (unknown) parameters. It then discusses more or less informative priors and more or less established likelihood-based computational methods (sampling- and variation-based), thus justifying the need for likelihood-free inference.