Over the last 10 years new types of polymeric materials with molecular recognition sites for low-weight organic substances have been prepared using the molecular imprinting approach. In this review paper, in particular, the recognition and transport properties of molecularly imprinted polymer (MIP) membranes prepared thus far are summarized and analyzed. Microporous and macroporous MIP membranes show the same receptor but largely different transport properties. The nature of selectivity of microporous MIP membranes is discussed and a descriptive model for transport selectivity via specific "gates" is developed. The high specificity and stability of MIPs render them as promising alternatives to enzymes, antibodies, and other natural receptors usually used in affinity chromatography and sensor technology. The application potential of MIP membranes, especially for affinity separations, membrane chromatography and membrane sensors, is outlined. Conclusions about the possibilities to improve their performance are presented. In general, these investigations open a way to the design of supramolecular devices that could perform highly selective functions such as recognition, transformation, transfer, regulation and allow signal and information processing.