Polymeric materials are ideal for modifying the properties of a wide range of surfaces due to their structural and chemical versatility. This dissertation describes the synthesis and utility of block copolymers and polymer brushes for patterning surfaces. The effect of a cyclic molecular architecture on feature size in phase separated block copolymer thin films is discussed, as well as the synthesis of acid-cleavable block copolymers for the fabrication of highly ordered nanoporous polymer thin films. In addition to polymers synthesized in solution for deposition onto surfaces, the synthesis of polymer brushes by surface-initiated polymerizations was also studied. A new light-mediated polymerization technique catalyzed by Ir(ppy)3 was employed as the surface-initiated polymerization technique. This polymerization is highly responsive to visible light and can be used to readily access patterns of polymer brushes. Using light as an external stimulus for brush growth or functionalization by a light-mediated atom transfer radical addition reaction, the molecular weight, architecture, grafting density, and chemical functionality of polymer brushes could be spatially controlled on surfaces. Finally, the synthesis of polymers by the Ir(ppy)3-catalyzed polymerization in solution was improved by utilizing a continuous flow reactor.