The review describes the evolution and present state of the use of accelerated heavy ion beams for investigation of track radiation effects and track membrane production at FLNR JINR. The research and development activity on track membranes (TMs) included studies of track formation process, latent track structure, environmental effects, sensitization of tracks, track etching, methods of membrane testing, designing and constructing facilities for membrane production. Some results on the physics and chemistry of ion tracks in polymers are described with the emphasis on the experiments performed during the last few years.