The mobility and self-diffusion of polymer molecules in concentrated systems or in the molten bulk state is largely controlled by entanglements between the molecules. These entanglements are a result of the chain-like nature of the molecules and of their extended, coil-like configuration. The conformation and mobility of polymer molecules in dilute solution—which are relatively well understood—are discussed; this leads to a consideration of self-diffusion in the more concentrated states and in the bulk polymer melt, and several special properties of polymers which are controlled and modified by the molecular self-diffusion are examined.