In this chapter, we introduce some of the tools that can be used to address these challenges. By considering how probabilistic models can be defined and used, we aim to provide some of the background relevant to the other chapters in this volume. The plan of the chapter is as follows. First, we outline the fundamentals of Bayesian inference, which is at the heart of many probabilistic models. We then discuss how to define probabilistic models that use richly structured probability distributions, introducing some of the key ideas behind graphical models, which can be used to represent the dependencies among a set of variables. Finally, we discuss two of the main algorithms that are used to evaluate the predictions of probabilistic models – the Expectation-Maximization (EM) algorithm, and Markov chain Monte Carlo (MCMC) – and some sophisticated probabilistic models that exploit these algorithms. Several books provide a more detailed discussion of these topics in the context of statistics (e.g., Berger, 1993; Bernardo & Smith, 1994; Gelman, Carlin, Stern, & Rubin, 1995), machine learning (e.g., Bishop, 2006; Duda, Hart, & Stork, 2000; Hastie, Tibshirani, & Friedman, 2001; Mackay, 2003), and artificial intelligence (e.g., Korb & Nicholson, 2003; Pearl, 1988; Russell & Norvig, 2002). Griffiths, Kemp, and Tenenbaum (in press) provide further information on some of the methods touched on in this chapter, together with examples of applications of these methods in cognitive science.