Strain localization zones in the form of shear bands or compaction bands in geomaterials are observed across scales from sub-millimetric (grain size) to kilometric scale (geological structures). Triggering and evolution of such narrow zones of localized deformation depend on many factors. The mechanical behavior of geomaterials is central for the formation of such zones. However, thermal, pore-pressure and chemical effects play a crucial role in shear and compaction banding. Moreover, the inherent heterogeneous microstructure of geomaterials plays a significant role during strain localization. As for faults, compaction bands significantly influence the stress field and fluid transport. In this paper, we shall review some recent advances in experimental testing and numerical modelling on strain localization in geomaterials. The effect of grain crushing as observed in deformation bands under high confinement can be introduced by combining Breakage models and higher order continuum theories leading to a new framework of constitutive models with evolving microstructure. A major difficulty of these models is to establish reliable methods for the calibration of the higher order parameters (such as the internal length) in laboratory experiments. An example of a direct calibration of these parameters based on Digital Image Correlation of images provided by X-Ray tomography is proposed for the study of compaction banding in a carbonate rock.