<sec>Laser-plasma interaction at intensities beyond 10<sup>22</sup> W/cm<sup>2</sup> enters a new regime where gamma-photon emission and the induced radiation-reaction effect dominate. In extreme laser fields, high energy electrons emit gamma-photons efficiently, which take considerable portion of energy away and impose strong reaction forces on radiating electrons. When the radiation power is comparable to the electron energy gained in a certain period of time, the radiation-reaction (RR) effect becomes significant, which fundamentally changes the picture of laser-plasma interaction. In this review article, we introduce the physics of radiation-reaction force, including both classical description and quantum description. The effects of stochastic emission and particle spins in the quantum-electrodynamics (QED) RR process are discussed. We summarize the RR-induced phenomena in laser-plasma interaction and some proposed measurements of RR. As a supplement, we also introduce the latest progress of producing spin polarized particles based on laser-plasma accelerations, which provides polarized beam sources for verifying the QED-RR effects.</sec><sec>In the classical picture, the RR force can be described by the Landau-Lifshitz (LL) equation, which eliminates the non-physical run-away solution from the Lorentz-Abraham-Dirac (LAD) equation. The damping force could induce the electron trajectories to instantaneously reverse, electrons to cool and even high energy electrons to be reflected by laser pulses. The latter leads to a “potential barrier” at a certain threshold that prevents the electrons of arbitrarily high energy from penetrating the laser field. In general, classical LL equation overestimates the RR effect, thus calling for more accurate quantum description.</sec><sec>When the emitted photon energy is close to the electron energy, radiation becomes discrete. Quantum effects arise such that the process, also known as nonlinear multi-photon Compton Scattering, must be considered in the strong-field QED picture. This is resolved in the Furry picture by using the laser-dressed Volkov state in the local constant cross-field approximation (LCFA). The QED model is applied to particle dynamics via Monte-Carlo (MC) sampling. We introduce the prominent feature of quantum RR-stochastic photon emission. It allows the processes forbidden in classical picture to emerge, such as quantum ‘quenching’, quantum ‘reflection’, etc. These observables validate the strong-field QED theory. Recently, there has been a rising interest in identifying the spin effect in the QED-RR force. We summarize the latest progress of this topic, showing that when spins are coupled with photon emission the electrons of different spin states undergo distinctive RR force. </sec><sec>The RR force has a significant effect on laser-plasma interaction. The review paper introduces recent QED-MC based PIC simulation results. Some key features include electron cooling in laser-driven radiation pressure acceleration and the radiation-reaction trapping (RRT) mechanism. In the RRT regime the laser pulse conveys over 10% of its energy to gamma-photons, facilitating the creation of a highly efficient gamma-ray source and electron-positron pair. In addition, the paper mentions the major efforts to measure the RR effect in recent years. It relies on high energy electrons either colliding with ultra-intense laser pulses or traversing crystals. Primitive observations indicate that existing theories do not match experimental results. Further investigation is required in both SF-QED theory and experiment.</sec><sec>Finally, the review paper discusses the idea of laser-driven polarized particle acceleration as a supplement. The all-optical approach integrates pre-polarized gas target into laser wakefield acceleration, offering a compact all-optical polarized particle source, which is highly favorable for strong-field QED studies, high-energy colliders and material science.</sec>