Can binding sites be produced in organic or inorganic polymers—similar to those in antibodies—which are able to recognize molecules and which may have catalytic action? In this article we review a method, analogous to a mechanism of antibody formation proposed earlier, by which in the presence of interacting monomers a cross-linked polymer is formed around a molecule that acts as a template. After removal of the template, an imprint containing functional groups capable of chemical interaction remains in the polymer. The shape of the imprint and the arrangement of the functional groups are complementary to the structure of the template. If chiral templates are used, the success of the imprinting process can be assessed by the ability of the polymer to resolve the racemate of the template molecule. Through optimization of the process has led to chromatographic separation factors of α = 4–8, and to base line separations. There is also great interest in the surface imprinting of solid materials and monolayers. In all cases, the structure of the polymeric matrix in the imprinted materials and the function of the binding groups are of crucial importance. The mechanisms of imprinting and molecular recognition of substrates are by now well understood. A large number of potential applications for this class materials are being intensively developed, for example in the chromatogrphic resolution of recemates, and as artificial antibodies, chemosensors, and selective catalysts. The use of similarly produced materials as enzyme models is also of great interest.