The martensitic transformation in copper-based alloys is thermoelastic, that is, the transformation progresses following the undercooling below the equilibrium temperature. In addition. a hysteresis is observed because of irreversible processes taking place during the transformation-retransformation path. These phenomena depend on the complexity of the problem and the related metastable phases being time dependent. In this report the most complex situation (temperature induced and stress free) is characterized via calorimetric and acoustic-emission measurements. Reduction in complexity is thus necessary if intrinsic phenomena are to be separated and quantified. Special experimental equipment with appropriate resolution is briefly outlined. The single-interface beta-18R transformation was chosen and then the complexity was increased progressively to characterize the intrinsic phenomena. Even in the single-interface transformation, an intrinsic thermoelasticity is found, which was ascribed to the interaction of growing martensite with the existing dislocations. In addition, the narrowest hysteresis width was measured. Nucleation and single-interface friction are distinguished. Dislocations show a paradoxical behavior in the martensitic transformation. Classically there is a perturbative component, but in samples without dislocations, breakdown of shape memory can be observed. The following rise in complexity relates the behavior of several martensite plates of the same type. The shape of the hysteresis cycles in stress-induced transformations can be very well described and simulated by using the elementary parameters measured in single-interface experiments. The experimental analysis shows the metastability is relatively important: it was found that the diffusional processes are important near room temperature or above. Several time-dependent contributions to the M-s and hysteresis cycles are introduced. Time constants were measured and predictable rules were established. Avoiding a stochastic interpretation, suitable algorithms to compute the time behavior of the M-s or the hysteresis cycles and internal loops were developed. Since the defects play a decisive role on the martensitic transformation characteristics, the crystallographic and energetic changes of the dislocations when embedded in the parent or martensitic phases were analyzed quantitatively. The interaction of the martensitic transformation with precipitates and the evolution of hysteresis width with cycling and precipitate size is studied. Finally, the two-shape memory effect is analyzed in terms of the interactions of the martensite with dislocations and other defects.