Fracture problems and damage processes have been widely studied in the last twenty years, starting from the pioneristic work of Griffith (and the later approach of Francfort - Marigò) to the more recent Gamma-convergence point of view developed by exploiting the Ambrosio - Tortorelli approximation for image recovery applied to the context of function of Bounded Deformation. In this talk we ill give a brief overview of the state of art of such a topic and we will end by presenting a recent approximation of fluid driven fracture based on a suitable correction of the classical energy with a lower order term that enable the introduction of several application. Some numerical experiments will also be discussed.