There is considerable interest currently in developing and understanding microstructural evolution, stability and deformation in the new class of highly concentrated, multi-principal element solid solution high entropy alloys. This overview provides a brief description of potential high temperature deformation mechanisms in such fine grained alloys, discusses the significance of diffusion, and compares the available experimental results with appropriate theoretical models. It is shown that diffusion is not substantially slower in such alloys, and that superplastic deformation follows the standard model established for conventional polycrystals. The data also suggest that deformation at higher stresses occurs by dislocation glide creep, followed by a power-law breakdown regime. It is necessary to exercise caution in interpreting spherical nanoindentation creep data, although some data on a nanocrystalline HEA suggest that deformation at room temperature occurs by Coble diffusion creep. Based on the available data and understanding, a deformation mechanism map is developed highlighting the dominance over different regimes of grain size and stress of Coble diffusion creep, superplastic flow, dislocation creep and power-law breakdown. (C) 2017 Elsevier B.V. All rights reserved.