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Understanding the physical mechanisms that control galaxy formation is a fundamental challenge in contemporary astrophysics. Recent advances in the field of astrophysical feedback strongly suggest that cosmic rays (CRs) may be crucially important for our understanding of cosmological galaxy formation and evolution. The appealing features of CRs are their relatively long cooling times and relatively strong dynamical coupling to the gas. In galaxies, CRs can be close to equipartition with the thermal, magnetic, and turbulent energy density in the interstellar medium, and can be dynamically very important in driving large-scale galactic winds. Similarly, CRs may provide a significant contribution to the pressure in the circumgalactic medium. In galaxy clusters, CRs may play a key role in addressing the classic cooling flow problem by facilitating efficient heating of the intracluster medium and preventing excessive star formation. Overall, the underlying physics of CR interactions with plasmas exhibit broad parallels across the entire range of scales characteristic of the interstellar, circumgalactic, and intracluster media. Here we present a review of the state-of-the-art of this field and provide a pedagogical introduction to cosmic ray plasma physics, including the physics of wave–particle interactions, acceleration processes, CR spatial and spectral transport, and important cooling processes. The field is ripe for discovery and will remain the subject of intense theoretical, computational, and observational research over the next decade with profound implications for the interpretation of the observations of stellar and supermassive black hole feedback spanning the entire width of the electromagnetic spectrum and multi-messenger data. [ABSTRACT FROM AUTHOR]