With the time, the number of studies associated to the martensitic transformation has been expanded; therefore, understand as this mechanism operates and as it confers different characteristics to diverse materials where it occurs, many studies has been conducted in different areas carrying out to discoveries at microstructural, kinetic and crystallographic level. This paper presents an overview of the martensitic transformation, beginning with a historical development, through a review on their morphology and kinetically characteristics, in addition to an analysis of the prospects of the studies carried out in the area, with a special interest in the phenomena of thermo-elasticity and shape memory.