One of the largest challenges of computational chemistry is calculation of accurate free energies for the binding of a small molecule to a biological macromolecule, which has immense implications in drug development. It is well-known that standard molecular-mechanics force fields used in most such calculations have a limited accuracy. Therefore, there has been a great interest in improving the estimates using quantum-mechanical (QM) methods. We review here approaches involving explicit QM energies to calculate binding affinities, with an emphasis on the methods, rather than on specific applications. Many different QM methods have been employed, ranging from semiempirical QM calculations, via density-functional theory, to strict coupled-cluster calculations. Dispersion and other empirical corrections are mandatory for the approximate methods, as well as large basis sets for the stricter methods. QM has been used for the ligand, for a few crucial groups around the ligand, for all the closest atoms (200-1000 atoms), or for the full receptor-ligand complex, but it is likely that with a proper embedding it might be enough to include all groups within ∼6 Å of the ligand. Approaches involving minimized structures, simulations of the end states of the binding reaction, or full free-energy simulations have been tested.