Many problems in geotechnical engineering involve large movements or rotations, examples include natural processes such as landslides, and man-made processes such as earthmoving and pile penetration. While the use of numerical modelling, primarily the finite element method (FEM), is now routine in geotechnical design and analysis, the limitations of conventional FEMs soon become apparent when attempting to model large deformation problems. For this reason, the search for alternatives remains a key goal of many geotechnical researchers, both to find accurate methods but also to develop efficient ones. In this review paper, prompted by Technical Committee 103 of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE), we survey the current state-of-the-art in numerical modelling techniques aimed at large deformation problems in geotechnics. The review covers continuum and discontinuum methods and provides a clear picture of what is and is not currently possible, which will be of use to both practitioners seeking suitable methods and researchers developing existing or new methods.