The rapid expansion of plastics and other polymeric materials into the general consumer market over the last few years is now being followed by an increasing use of these materials in more severe engineering applications. It is becoming necessary therefore for engineers to develop a familiarity with these materials commensurate with that which they already have for more conventional engineering materials. In many ways the physical properties of polymeric materials are highly complex and their description and relation to structure present real problems. This article presents, in a simple way, some of the background to our current level of understanding of the relation between structure and mechanical properties; gives some examples of how polymeric materials are being used; and discusses some of the problems of designing in these materials, which present a real challenge to both the physicist and the engineer.