In this review paper, we outline the principles of Monte Carlo simulation of fluid mixtures, with emphasis on methods for calculation of free energies and phase equilibria. We begin with a brief introduction to common intermolecular potential models. We discuss density-dependent potentials that can accurately represent properties over a wide range of densities. A number of Monte Carlo techniques are outlined in the main section of the paper. After an introduction to importance sampling, we discuss interfacial simulations, Widom test particle insertions and Grand Canonical Monte Carlo as well as the Gibbs ensemble method. Recent developments, including configurational-bias sampling, Gibbs-Duhem integration, thermodynamic-scaling Monte Carlo and finite-size scaling methods are the primary focus of the article. We close with a summary and a discussion of future prospects.