In ligandâ receptor binding it is generally accepted that molecular recognition takes place in a region near the molecular surface and involves both the three-dimensional shape of the surface and the distributions of certain properties on the surface. Consequently, molecular surfaces and surface properties have found extensive application in many aspects of in silico drug design, including virtual screening and the development of quantitative structureâ activity relationships, and often play a central role in questions related to molecular similarity. This chapter reviews the various ways in which molecular surfaces are modelled, the surface properties that have been studied and the methods that have been developed for their analysis and application. Several of these methods involve the local extrema of surface properties and a systematic procedure for analysing these through the Morse-Smale complex of the gradient vector field of the property is outlined.