Energetic plasmas are found in all astrophysical environments. However, beyond the solar system, our understanding of cosmic plasma dynamics has remained quite poor. This paper presents an attempt to explore a new description of various high-energy astrophysical phenomena, observed from galaxies and galaxy clusters, in terms of plasma magnetohydrodynamics. In this context, three specific topics are described; diffuse hot plasmas filling the Milky Way, plasma acceleration by giant black holes, and hot plasmas of galaxy clusters with relevance to cosmology.