Binding free energy predictions have the potential to play pivotal roles in the drug discovery process, ranging from aiding selection of hit molecules from large databases of compounds to optimizing lead structures. Calculation of relative binding free energies from molecular simulations (e.g., molecular dynamics or Monte Carlo simulations), though computationally intensive, have proved their worth in a number of pharmaceutical applications. Despite this, it is now clear that, in many cases, the methods typically used in such simulations to model molecular interactions have significant limitations. For example, in protein–ligand systems in which charge transfer or polarization are important, or where a metal ion is present in the binding site, conventional molecular mechanics (MM) methods may not represent binding accurately. Methods based on quantum mechanics (QM), for all or part of the system, are potentially more accurate. This chapter reviews recent advances in the growing field of calculating or predicting binding free energies using a quantum mechanical (i.e., quantum chemical, electronic structure) treatment of all or part of the system, for example, a QM description of the ligand alone (or with part of the binding site), coupled to a MM treatment of the protein (QM/MM calculations) or a QM description of the entire protein–ligand complex. Keywords: drug design; free-energy calculations; protein–ligand simulation; quantum mechanics/molecular mechanics