Computational methods available for the calculation of relative and absolute binding affinities (free energy simulations, continuum electrostatics, linear interaction energy approximations, and empirical solvation models) are reviewed together with recent applications to biological systems. The decomposability of the binding free energy into physically meaningful components is examined and results obtained for these components are presented. Some of these components, such as the direct interactions, the translational / rotational entropy loss, and the desolvation free energy are well recognized. Recent calculations have shown that the translational / rotational entropy loss is not as large as some theoretical calculations have previously suggested because of substantial residual movements in the bound complex. Recent work also points to the importance of contributions that are often neglected in binding affinity calculations, such as the protein reorganization energy and, for flexible ligands, the ligand reorganization energy. Future work should concentrate on the improvement of the energy functions and simulation protocols for the achievement of more precise and accurate predictions.