Computer simulations of biomolecules have been improving at a pace that is faster than Moore’s law for microprocessors in the last few decades. Thanks to advances in theory, hardware, and algorithms it is increasingly possible to study biological processes at relevant spatial and temporal resolutions, and to exploit simulation for quantitative predictions. One area that can potentially benefit greatly from such computational predictions is that of drug discovery. Since the inception of the concept of rational drug design, the prediction of how tightly an organic molecule binds to a macromolecular partner has been one of the chief objectives of computational chemistry. Computers already play a fundamental support role during the drug discovery process, and today many novel approaches that aim at studying the details of drug binding and predicting binding affinity are being actively investigated. In this thesis, I report a series of studies that aim to evaluate the potential utility of free energy calculations based on molecular simulations for drug design. In particular, I focus on the prediction of small-molecule binding affinities to the epigenetic target of bromodomains. Bromodomains are small protein modules that have been found in 46 human proteins involved in gene regulation. Given their role in various diseases, in particular cancer and inflammation, a number of bromodomain inhibitors are currently being investigated both in the laboratory and the clinic. Here, it is shown how thorough calculations based on explicit-solvent simulations and all-atom force fields can accurately reproduce binding free energies for this protein family. Rigorous free energy calculations are also compared to more approximate methods based on the post-processing of the simulation trajectories in implicit solvent. Finally, a recently proposed method for the estimation of water binding free energy is employed to study water displaceability from bromodomain binding pockets.</p