Shape memory polymers (SMPs) are a novel class of shape memory materials which can store a deformed (temporary) shape and recover an original (permanent) shape under a shape memory thermomechanical loading-unloading cycle. The deformation mechanisms of SMPs are very complicated, but the SMPs also have a lot of advantages and the widespread application value and prospect. So developing proper constitutive models that describe thermomechanical properties of SMPs and the shape memory effect is very challenging and of great theoretical and application value. Based on the deformation mechanisms and considerable experimental investigations of SMPs, researchers have developed many constitutive models. This article investigates the deformation mechanism and introduces the recent research advance of the constitutive models of thermal-sensitive SMPs. Special emphases are given on the micromechanical constitutive relations in which the deformation is considered being based on the microstructure of the SMPs. Finally, the lack of research and prospects for further research are discussed. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci 123: 1502-1508, 2012