Metals processed by severe plastic deformation [SPD] techniques, such as equal-channel angular pressing [ECAP] and high-pressure torsion [HPT], generally have submicrometer grain sizes. Consequently, they exhibit high strength as expected on the basis of the HallPetch [H-P] relationship. Examples of this behavior are discussed using data on Ti, Al-Mg 1 and Ni. These materials typically have grain size above ~50 nm where softening is not expected. An increase in strength is usually accompanied by a decrease in ductility. High strength and ductility can be achieved simultaneously by imposing high strains to give both ultrafine grain sizes and a high fraction of high-angle grain boundaries. An example is presented for a cast Al-7% Si alloy processed by HPT. In some cases, SPD may produce a fine grain size but also lead to a weakening due to microstructural changes as in ECAP of an Al-7034 alloy and HPT of Zn-22% Al. In SPD-processed materials, grain boundary segregation and nanostructural features are present which may lead to higher strengths than those predicted by the H-P relationship in some alloys having nano grain sizes.