Hydrodynamic instabilities triggered by a shock wave manifest in natural occurrences and engineering realms, serving as vital tools for exploring gas dynamics, vortex dynamics, and turbulence. However, suppressing these instabilities poses a persistent challenge in applications like inertial confinement fusion. The domain of “shock-gas-layer interaction” has seen rapid progress, fueled by advancements in experimental methods, numerical modeling, and theoretical insights. Within this realm, a spectrum of wave patterns and hydrodynamic instabilities has been unveiled, encompassing reverberating waves, feedthrough phenomena, abnormal behaviors, and freeze-out Richtmyer-Meshkov instability. This discussion delves into recent strides made in understanding shock-gas-layer interactions, with a focus on the feedthrough mechanism, reverberating waves, and their cascade of additional instabilities. Moreover, we outline the criteria for mitigating hydrodynamic instabilities.