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The use of X-ray and neutron reflectivity to study polymers in the condensed state and in solutions is revieved in this article. Basic theoretical and experimental concepts of specular reflectivity are presented. Research in the application of neutron and X-ray reflectivity is discussed along with the relevance of these studies to important issues in polymer science. These include investigations of ordered and disordered homopolymers and block copolymers in solution and in the condensed state. Finally, a discussion of off-specular, diffuse scattering is presented with its potential use in polymer science.