Thermoplastic elastomers (TPEs) form a class of soft polymeric material of great practical interest. They typically show the high elongations to break and low stiffnesses associated with natural and synthetic rubbery materials, and hence are of value in a wide range of products where flexibility and resilience are required. But whereas in traditional rubbery materials (those available more than 50 years ago) connectivity between the flexible polymer molecules is achieved by chemical crosslinking, this is not the case in TPEs. Instead, in these materials, the chemical architecture of the polymer itself is tailored so as to provide a physical crosslinking effect.