In this talk I will describe a class of minimization problems arising in modelling shape memory alloys. I will start with a shape memory material illustration, followed by a simple one dimensional model of it. Its extensions in 2D and 3D will help us understand the energetic mechanism behind the formation of twin patterns in physical experiments. By means of sharp upper and lower bounds, we show that the experimentally observed structures provide optimal energy scaling law. Furthermore, under certain assumptions we will see that some of these patterns are true energy minimizers - a rare find in problems of this type! I will also discuss the extension of the linear elastic models for two twins to model multiscale patterns, which appear in recent physical experiments and involve mixing of four twins.