Materials modeling has always been a challenging issue. Many complexities rise in such modelings, like non-linear material behavior, complex physics, and large deformation, coupled with multiphysics phenomena. Moreover, materials often exhibit rich behavior in response to thickness, hindering the use of classical simplifications, and imposing the need for an extremely refined mesh when using classical simulation techniques. Model reduction techniques appeared as a suitable solution to alleviate computational time. Many applications and material-forming processes benefit from the advantages offered by model reduction techniques including solid deformation, heat transfer, and fluid flow. Moreover, the recent development in data-driven modeling has opened novel possibilities in materials modeling. In fact, a correction or an update of the simulation using data modeling has led to the formation of the so-called “digital twin” models, improving the simulation with data-driven modeling. Data-driven modeling of materials for which current models are inaccurate also became possible through the use of machine learning algorithms.