Abstract: Recent findings have linked low hysteresis in shape memory alloys with phase compatibility between austenite and martensite. In order to investigate the evolution of microstructure as the phase compatibility increases and the hysteresis is reduced, transmission electron microscopy was used to study the alloy system Ti50Ni50-xPdx where the composition is systemically tuned to approach perfect compatibility. Changes in morphology, twinning density and twinning modes are reported along with special microstructures occurring when the compatibility is achieved. In addition, the interface between austenite and a single variant of martensite was studied by high-resolution and conventional electron microscopy. The atomically sharp, defect free, low energy configuration of the interface suggests that it plays an important role in the lowering of hysteresis. Finally, dynamical modeling of the martensitic transformation using the phase-field micro-elasticity model within the geometrically linear theory succeeded in reproducing the change in microstructure as the compatibility condition is satisfied. Latest results on the extension of these findings in other Ni-Ti based ternary/quaternary systems are also reported.