Polymers are materials worthy of study both because of their unique properties and because of their common occurrence in industrial products and in biological systems. The attention focused on them has been rewarded by an increased amount of success in establishing the relationships between their complex physical properties and their molecular structure. This article is concerned with a particular aspect of these investigations, the Theological properties of polymers in the liquid state. There has been an increase of activity in this field during the last fifteen years, which is the period covered by this review. The interested reader is directed to earlier reviews and articles that discuss related subject material. We begin with a qualitative description of a rheological experiment which demonstrates the mechanical response of polymers as well as introduces some of the essential phenomena which need to be explained. When a small shearing force is applied to a high-molecular-weight polymer liquid, it deforms rapidly. At first, the material acts like a rubbery solid and, if the stress is quickly removed, it essentially recovers its original shape. The constant relating the applied stress, σ, and the initial deformation or strain, γ, is the elastic modulus, GN, often referred to as the plateau modulus.