Mounting evidence is pointing to some emerging novel behaviors of metals with ultrafine-grain (UFG) and/or nanocrystalline (NC) microstructures. One such novel behavior is related to the thermodynamic and kinetic aspects of plastic response in the UFG/NC regime. Two inter-related parameters, viz., the strain rate sensitivity (SRS) and the activation volumes of plastic deformation, are used as fingerprints for the thermodynamics and kinetics of plastic deformation. Changes of these parameters with grain size may indicate transition of plastic deformation mechanisms. Therefore, investigations of these phenomena may bring out new strategies for ingenious design and synthesis of UFG/NC materials with desirable properties. In this article, we present a critical review on the experimental results and theories associated with the SRS of UFG/NC metals with different lattice structures, and the influences on some constitutive responses.