Studies on constitutive modeling and numerical analysis methods have been well developed. Nowadays, numerical and analytical methods play a very important role in Geotechnical Engineering and in a related activity called Computational Geotechnics. Due to large deformations and failure, however, several issues are encountered in Computational Geotechnics. They include constitutive modeling and its calibration, mechanical instabilities: strain localization and progressive failure, the modeling of chemo-thermo-hydro-mechanical coupled behavior, and the verification and the validation of the mathematical modeling. In the present paper, we deal with the recent progress that has been made to solve these problems, in particular, the constitutive modeling of soil for rate-dependent models with structural degradation, strain localization, liquefaction of soil and their applications in the context of large deformations and the failure of geomaterials.