The classical formulations for material forming either in the solid or in the liquid state are briefly recalled, in terms of material constitutive behavior, friction law, integral forms and finite element discretization. A few important numerical issues are discussed, including meshing, remeshing and adaptivity, parallel computing and coupling between work-piece and tools. Five examples of applications of finite element models to new processes are presented: friction stir welding, hot stamping of quenchable steels, tube hydroforming, thixoforming and self piercing riveting. It is concluded that many new forming processes can be designed and optimized much more effectively using the numerical simulation technology.