Shape Memory Alloys (SMAs) is a class of smart materials with the ability to remember the original shape. SMAs exhibit stress-induced martensitic transformation through twinning which is an important deformation mechanism that renders strength and ductility. Tailoring the capability of alloys for deformation twinning enables to optimise their mechanical performance. This paper presents a comprehensive review on the effect of internal and external parameters on the twinning propensity. Among these parameters, the effect of the composition, grain size, temperature and strain rate will be explored. In addition the use of shape memory phase as a strategy to improve the ductility of metallic use memory behaviour is of great importance to develop SMAs for multiple applications including mechanical, automotive, aerospace, civil and biomedical industries. A tentative outlook about the challenges and proposed solutions will be also discussed.