Many spectacular phenomena in the high-energy Universe, such as bright, rapid gamma-ray flares, are powered by complex collective plasma processes around relativistic objects: neutron stars and black holes. While our understanding of such processes has greatly benefitted from traditional (space, solar, laboratory) plasma research, the physical conditions near black holes and neutron stars are so extreme that conventional intuition often fails, and a richer physics framework is required. Extreme astrophysical plasmas are relativistic, interact strongly with radiation, and may be subject to QED (e.g., pair-production) effects. Understanding how this additional physics affects collective plasma processes (waves and instabilities, magnetic reconnection, turbulence, etc.) is the main goal of _*Extreme Plasma Astrophysics*_. Exploration of this new exciting frontier is now advancing rapidly, thanks to strong observational motivation, vigorous theoretical efforts, and the advent of novel first-principles relativistic kinetic plasma simulation codes incorporating radiation and QED effects. Laser-plasma experiments will soon also contribute to this revolution. In this talk, I will review the recent progress in this burgeoning new field, focusing on theoretical and computational studies of relativistic radiative magnetic reconnection and turbulence and their astrophysical applications to neutron-star magnetospheres and black-hole coronae and jets. I will also outline key theoretical challenges and future directions of Extreme Plasma Astrophysics.
