Current developments in kinetic and thermodynamic stabilization of grains in nanostructured metals, alloys, and compounds are generalized and discussed in detail. As applied to the thermodynamic approach, attention has recently shifted from using the regular solution approximation to estimating thermodynamic properties of nanomaterials by considering both inner regions of nanograins and their grain boundaries. This situation is discussed and examples for alloys based on iron, copper, tungsten, and other elements are presented. Experimental information about behavior of nanomaterials subjected to radiation or oxidation is considered, along with recent experiments on abnormal grain growth.