Ligand binding affinity prediction is one of the most important applications of computational chemistry. However, accurately ranking compounds with respect to their estimated binding affinities to a biomolecular target remains highly challenging. We provide an overview of recent work using molecular mechanics energy functions to address this challenge. We briefly review methods that use molecular dynamics and Monte Carlo simulations to predict absolute and relative ligand binding free energies, as well as our own work in which we have developed a physics-based scoring method that can be applied to hundreds of thousands of compounds by invoking a number of simplifying approximations. In our previous studies, we have demonstrated that our scoring method is a promising approach for improving the discrimination between ligands that are known to bind and those that are presumed not to, in virtual screening of large compound databases. In new results presented here, we explore several improvements to our computational method including modifying the dielectric constant used for the protein and ligand interiors, and empirically scaling energy terms to compensate for deficiencies in the energy model. Future directions for further improving our physics-based scoring method are also discussed.