We have developed a new class of synthetic membranes that consist of a porous polymeric support that contains an ensemble of gold nanotubules that span the complete thickness of the support membrane. The support is a commercially available microporous polycarbonate filter with cylindrical nanoscopic pores. The gold nanotubules are prepared via electroless deposition of Au onto the pore walls; i.e., the pores acts as templates for the nanotubules. We have shown that by controlling the Au deposition time, Au nanotubules that have effective inside diameters of molecular dimensions (<1 nm) can be prepared. Hence, these membranes are a new class of molecular sieves. In addition, because these membranes are composed of an electronically conductive material, excess charge can be applied to the tubules by electrochemical charging in an electrolyte solution. We have shown that this allows for control of ion-transport selectivity in these membranes. Finally, because the tubules are composed of gold, well-known Au-thiol chemistry can be used to change the chemical environment within the tubules. Via this route chemical transport selectivity can be introduced into these membranes. This paper reviews progress on size-based, charge-based, and chemical-interaction-based transport selectivity in this new class of membranes.