The issue of laser plasma instabilities (LPIs) including stimulated Raman scattering, stimulated Brillouin scattering and so on is one of the most fascinating subjects in laser plasma physics. In particular, LPIs may cause significant laser energy loss and produce hot electrons to preheat fusion targets, which affect target compression and fusion energy gain in laser-driven inertial confinement fusion. Recent experiments carried out on the National Ignition Facility, the largest laser facility in the world for laser fusion, indicate that the understanding and the control of LPIs are essential to the realization of laser fusion. In this paper, we present a review on recent studies of LPIs. Firstly, we retrospect the classical theoretical model of LPIs, which offers a good estimation of growth rate in the linear development stage. Then, we discuss some progresses on the understanding of LPIs in more complex and real scenarios, such as LPI development in the nonlinear regions, cascaded LPIs, multi-beam LPIs, and nonlinear couplings between LPIs. Following the exploration of LPI physics, we emphasize on the strategies for the control of LPIs, including beam smoothing techniques, temporal profile shaping, broadband laser, laser polarization rotation, external magnetic field and so on.
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