This Perspective describes recent progress in the area of the molecular simulation of the interactions of hydrophobic and hydrophilic solutes with membranes. The ability to predict drug solubility prior to synthesis is an extremely desirable goal for pharmaceutical research. A major advantage of molecular dynamics is the ability to computationally probe both the drug solubility as well as the pathway for the transport of drugs across membranes. Computational methods to predict the interaction free energy of solutes with membranes have advanced significantly in recent years and can characterize the intra- and intermolecular state of the drug as well as perturbations of the drug to the membrane environment itself. In addition to a brief review on computational methods to characterize the transport of drugs across membranes, we will highlight recent discoveries and discuss the challenges and opportunities in the field.