Diffusion of low-molecular substances in high polymers has been the object of study by many Soviet and other investigators during the past two decades. Included is the work of Reitlinger, Zhurkova, Ryskin, Malinskii, and Vasenin in the Soviet Union, and Barrer, Crank, Long, Auerbach, van Amerongen, McCall, Shtamm, and many other authors elsewhere. By way of contrast, the effects of self-diffusion in polymers and diffusion of polymer in polymer (inter-diffusion) have been given little study because of the great experimental difficulties and the complexity of theoretical explanations. Meanwhile, these effects have considerable scientific and practical significance. As will be seen hereafter, very many properties of polymers are associated in some manner with diffusivity of macromolecules or their segments. No less important is the tendency toward self- and inter-diffusion of polymers in processing and use. The aim of this review is to correlate data concerning self- and inter-diffusion of polymers containing elastic molecules (elastomers), available in several studies, and to suggest further paths for investigation of this problem.