Shape similarity is a key concept and requirement for molecular recognition. As a result, much research has been undertaken to develop methods to represent molecular shape and to quantify the shape similarity between molecules. A great variety of shape descriptions and similarity comparison approaches have been developed, ranging from explicit representations using intersecting atom-centered spheres and molecular superposition to abstract statistical representations that allow alignment-free comparisons. Several of these methods have sufficient computational performance to allow shape similarity searches over extremely large compound databases as a ligand-based virtual screening (VS) technique. As with other approaches to VS, the relative performance of shape similarity methods is dataset and problem specific, with each approach having its merits and limitations and no one approach showing a clear and consistent advantage over the others. Again, as with other VS approaches, most reports of performance are in the context of retrospective validation studies, which show competitive performance against target-based and two-dimensional methods. Prospective studies are rarer in the literature, but a number of successes have been reported. Intensive research continues in the search for improved representations of shape, partial shape matching, and approaches to address the challenges imposed by ligand and target flexibility. C 2012 John Wiley & Sons, Ltd.