We have defined a molecular surface representation that describes precisely and concisely the complete molecular surface. The representation consists of a limited number of critical points disposed at key locations over the surface. These points adequately represent the shape and the important characteristics of the surface, despite the fact that they are modest in number. We expect the representation to be useful in areas such as molecular recognition and visualization. In particular, using this representation, we are able to achieve accurate and efficient protein-protein and protein-small molecule docking.