Abstract: Physical conditions in plasma environments of exotic relativistic objects like neutron stars and black holes can be extreme and very different from those in more familiar, traditional heliospheric and laboratory plasmas. The richer physics of these extreme astrophysical plasmas includes the effects of special and general relativity, pair-plasma composition, strong interaction between plasma particles and high-energy photons, and, in the most extreme cases, QED effects like pair production and annihilation. Understanding how these “exotic” physical effects modify fundamental collective plasma processes — such as waves, instabilities, magnetic reconnection, shocks, turbulence — is the scope of Extreme Plasma Astrophysics — an challenging and exciting frontier of modern physics. I will review the recent rapid progress in exploring this frontier, motivated by spectacular astrophysical discoveries and enabled by recent computational advances like the development of novel kinetic plasma codes incorporating radiation and pair-creation effects, in combination with vigorous, concerted theoretical efforts. Examples include new breakthroughs in our understanding of radiative relativistic magnetic reconnection and turbulence, with applications to accreting black holes and neutron star magnetospheres. I will also outline the key future directions of this burgeoning field, including for laboratory studies.