Polymers provide a versatile platform for mimicking various aspects of physiological extracellular matrix properties such as chemical composition, rigidity, and topography for use in cell and tissue engineering applications. In this review, we provide a brief overview of patterning methods of various polymers with a particular focus on biocompatibility and processability. The materials highlighted here are widely used polymers including thermally curable polydimethyl siloxane, ultraviolet-curable polyurethane acrylate and polyethylene glycol, thermo-sensitive poly(N-isopropylacrylamide) and thermoplastic and conductive polymers. We also discuss how micro- and nanofabricated polymeric substrates of tunable elastic modulus can be used to engineer cell and tissue structure and function. Such synergistic effect of topography and rigidity of polymers may be able to contribute to constructing more physiologically relevant microenvironment.