This overview highlights some salient features of one of the most popular severe plastic deformation techniques: high-pressure torsion (HPT). It focuses on the unresolved challenging problems of HPT. The problems selected touch upon some fundamental questions of mechanics of plasticity, fracture, and friction that are at the core of the HPT process. The scientific significance of these problems and the proposed pathways to resolving them are discussed. The article is meant to promote the use of HPT as a potent tool for studying plasticity at large strains theoretically and also as a practical method enabling novel micromanufacturing routes.