Inertial fusion energy(IFE)has been considered a promising,nearly inexhaustible source of sustainable carbon-free power for the world’s energy future.It has long been recognized that the control of hydrodynamic instabilities is of critical importance for ignition and high-gain in the inertial-confinement fusion(ICF)hot-spot ignition scheme.In this mini-review,we summarize the progress of theoretical and simulation research of hydrodynamic instabilities in the ICF central hot-spot implosion in our group over the past decade.In order to obtain sufficient understanding of the growth of hydrodynamic instabilities in ICF,we first decompose the problem into different stages according to the implosion physics processes.The decomposed essential physics processes that are associated with ICF implosions,such as Rayleigh-Taylor instability(RTI),Richtmyer-Meshkov instability(RMI),Kelvin-Helmholtz instability(KHI),convergent geometry effects,as well as perturbation feed-through are reviewed.Analytical models in planar,cylindrical,and spherical geometries have been established to study different physical aspects,including density-gradient,interface-coupling,geometry,and convergent effects.The influence of ablation in the presence of preheating on the RTI has been extensively studied by numerical simulations.The KHI considering the ablation effect has been discussed in detail for the first time.A series of single-mode ablative RTI experiments has been performed on the Shenguang-Ⅱlaser facility.The theoretical and simulation research provides us the physical insights of linear and weakly nonlinear growths,and nonlinear evolutions of the hydrodynamic instabilities in ICF implosions,which has directly supported the research of ICF ignition target design.The ICF hot-spot ignition implosion design that uses several controlling features,based on our current understanding of hydrodynamic instabilities,to address shell implosion stability,has been briefly described,several of which are novel. Inertial fusion energy (IFE) has been considered a promising, nearly inexhaustible source of sustainable carbon-free power for the world’s energy future. It has long been recognized that the control of hydrodynamic instabilities is of critical importance for ignition and high-gain in the inertial-confinement fusion (ICF) hot-spot ignition scheme. In this mini-review, we summarize the progress of theoretical and simulation research of hydrodynamic instabilities in the ICF central hot-spot implosion in our group over the past decade. In order to obtain sufficient understanding of the growth of hydrodynamic instabilities in ICF, we first decompose the problem into different stages according to the implosion physics processes. The decomposed essential physics processes that are associated with ICF implosions, such as Rayleigh-Taylor instability (RTI), Richtmyer -Meshkov instability (RMI), Kelvin-Helmholtz instability (KHI), convergent geometry effects, as well as perturbation feed-through are are.Analyti cal models in planar, cylindrical, and spherical geometries have been established to study different physical aspects, including density-gradient, interface-coupling, geometry, and convergent effects. The influence of ablation in the presence of preheating on the RTI has been extensively studied by numerical simulations. The KHI considered the ablation effect has been discussed in detail for the first time. A series of single-mode ablative RTI experiments has been performed on the Shenguang-II laser facility. The theory and simulation research provides us the physical insights of linear and weakly nonlinear growths, and nonlinear evolutions of the hydrodynamic instabilities in ICF implosions, which has directly supported the research of ICF ignition target design the. ICF hot-spot ignition implosion design that uses several controlling features, based on our current understanding of hydrodynamic instabilities, to address shell implosion stability, has been briefly described, several of which are novel.