Accurate predictions of binding free energies from computer simulations are an invaluable resource for understanding biochemical processes and drug action. The primary aim of the work described in the thesis was to predict and understand ligand binding to several proteins of major pharmaceutical importance using computational methods. We report a computational strategy to quantitatively predict the effects of alanine scanning and ligand modifications based on molecular dynamics free energy simulations. A smooth stepwise scheme for free energy perturbation calculations is derived and applied to a series of thirteen alanine mutations of the human neuropeptide Y1 G-protein coupled receptor and a series of eight analogous antagonists. The robustness and accuracy of the method enables univocal interpretation of existing mutagenesis and binding data. We show how these calculations can be used to validate structural models and demonstrate their ability to discriminate against suboptimal ones. Site-directed mutagenesis, homology modelling and docking were further used to characterize agonist binding to the human neuropeptide Y2 receptor, which is important in feeding behavior and an obesity drug target.  In a separate project, homology modelling was also used for rationalization of mutagenesis data for an integron integrase involved in antibiotic resistance. Blockade of the hERG potassium channel by various drug-like compounds, potentially causing serious cardiac side effects, is a major problem in drug development. We have used a homology model of hERG to conduct molecular docking experiments with a series of channel blockers, followed by molecular dynamics simulations of the complexes and evaluation of binding free energies with the linear interaction energy method. The calculations are in good agreement with experimental binding affinities and allow for a rationalization of three-dimensional structure-activity relationships with implications for design of new compounds. Docking, scoring, molecular dynamics, and the linear interaction energy method were also used to predict binding modes and affinities for a large set of inhibitors to HIV-1 reverse transcriptase. Good agreement with experiment was found and the work provides a validation of the methodology as a powerful tool in structure-based drug design. It is also easily scalable for higher throughput of compounds.