Since the end of the last century a lot of research on ductile damaging and fracture process has been carried out. The interest and the attention on the topic are due to several aspects. The margin to reduce the costs of production or maintenance can be still improved by a better knowledge of the ductile failure, leading to the necessity to overcome traditional approaches. New materials or technologies introduced in the industrial market require new strategies and approaches to model the metal behavior. In particular, the increase of the computational power together with the use of finite elements (FE), extended finite elements (X-FE), discrete elements (DE) methods need the formulation of constitutive models capable of describing accurately the physical phenomenon of the damaging process. Therefore, the recent development of novel constitutive models and damage criteria. This work offers an overview on the current state of the art in non-linear deformation and damaging process reviewing the main constitutive models and their numerical applications.