We have developed a new class of synthetic membranes that consist of a porous polymeric support that contains an ensemble of gold nanotubes that span the thickness of the support membrane. The support is a commercially-available microporous polycarbonate filter with cylindrical nanoscopic pores. The gold nanotubes are prepared by electroless deposition of Au onto the pore walls, that is, the pores acts as templates for the nanotubes. We have shown that by controlling the Au deposition time, Au nanotubes that have effective inside diameters of molecular dimensions (<1 nm) can be prepared. These nanotube membranes can be used to cleanly separate small molecules on the basis of molecular size. Furthermore, use of these membranes as a novel electrochemical sensor is also discussed. This new sensing scheme involves applying a constant potential across the Au nanotube membrane and measuring the drop in the transmembrane current upon the addition of the analyte. This paper reviews our recent progress on size-based based transport selectivity and sensor applications in this new class of membranes.