The properties of asymmetrical nanopores prepared by chemical etching of tracks of accelerated heavy ions are studied. Procedures are developed for controlling the size and shape of pores within wide limits. The presence of charged functional groups on pore walls is an intrinsic property of track membranes, which makes them a convenient object for studying electrokinetic phenomena in nanocapillaries. In electrolyte solutions, the asymmetrical “track” membranes demonstrate the diode effect. Two methods for fabricating asymmetrical nanopores in polyethylene terephthalate films are proposed and introduced into practice. Specific features of both methods, their advantages and drawbacks are considered. In addition to the brief survey of available information on diode-like track membranes, the new results on the mechanism of pore formation and the peculiarities of their geometry and electrokinetic properties are discussed. The emerging and potential applications of track membranes with asymmetrical pores are discussed briefly.