Thermo-sensitive polymers, which are capable to exhibit a dual-, triple-, or multi-shape effect or a temperature-memory effect (TME), characterized by a controlled shape change in a predefined way, are of current technological interest for designing and realization of actively moving intelligent devices. Here, the methods for the quantitative characterization of shape-memory effects in polymers and recently developed thermomechanical modeling approaches for the simulation of dual-, triple-, and multi-shape polymers as well as materials that exhibit a TME are discussed and some application oriented models are presented. Standardized methods for comprehensive quantification of the different effects and reliable modeling approaches form the basis for a successful translation of the extraordinary achievements of fundamental research into technological applications. (c) 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013