The martensitic microstructure of shape memory alloys is an aggregate of self accommodating plate groups. The principal character of this aggregate is its demonstration of pseudoplasticity, wherein a macroscopic shape change is brought about by extensive rearrangement and reorientation of the self accommodating martensite variants, and that of microstructural reversibility, wherein the polyvariant microstructure transforms back to the original grain of the parent phase after pseudoplastic deformation. These aspects of the shape memory intermetallic alloys are intriguing and, to a great extent, unsolved. The aim of this paper is to show that the underlying crystallographic interrelationships of the self accommodating microstructure of intermetallic alloys are responsible for the observed effect. The paper will discuss the relation between autocatalytic nucleation and self accommodation, the relation between microstructural reversibility and intervariant interfaces of the martensitic microstructure and the manifestations of microstructural irreversibility using results from the microstructural examination of the self accommodating microstructures.