This paper will review the grain growth in nanocrystalline materials with emphasis on the grain size stabilization that can result from solute additions. The grain growth in nominally pure nanocrystalline metals will be presented followed by descriptions of the stabilization of nanocrystalline grain sizes by kinetic approaches and thermodynamic strategies. The descriptions of nanocrystalline grain size by solute additions will be taken from the literature as well as from recent research in the authors' laboratory. Examples of kinetic stabilization, which involves reduction of the grain boundary mobility, include second phase drag, solute drag, chemical ordering, and grain size stabilization. The thermodynamic stabilization, which is due to the lowering of the specific grain boundary energy by solute segregation to the grain boundaries, will be described for systems including Pd-Zr, Fe-Zr, Ni-W, Ni-P, and Co-P. Recrystallization during grain growth will be presented for the Ti-N system. Finally, a summary of alloys where nanocrystalline grain sizes can be maintained at annealing temperatures close to the melting point will be presented.