Abstract: Laser fusion represents a promising approach to achieving controlled nuclear fusion, yet the rapid growth of hydrodynamic instabilities during the implosion remain a primary cause of performance degradation and a critical bottleneck for attaining higher gain. In inertial confinement fusion, the ablation front is among the most unstable interfaces, and its perturbation evolution critically affects target compression and threatens shell integrity. This article systematically reviews the fundamental physics and recent advances in ablative hydrodynamic instabilities, with a particular emphasis on the ablation-front dynamics. The basic concepts and key processes of laser-driven implosions are first outlined, covering the ablation, acceleration, deceleration, and stagnation phases. The stringent ignition requirements—namely, high convergence ratio, high implosion velocity, and high compression—are then described, along with the associated instability risks that arise under such extreme conditions. After briefly revisiting the well-established theories of the ablative Richtmyer-Meshkov instability (RMI) and the ablative Rayleigh-Taylor instability (RTI), we present three major recent advances that integrate theoretical analysis and experimental validation. First, a stage dominated by ablation-front deformation is identified in the early radiation-driven phase, preceding the conventional ablative RMI; this deformation sets the initial conditions for subsequent instability evolution. Second, during the transition from the ablative RMI to the ablative RTI, non-exponential (secular) growth dynamics induced by the return of rarefaction waves are experimentally confirmed, and a wave-number-dependent “freeze” phenomenon is predicted for specific perturbation modes, which may help suppress unwanted growth. Third, a modified fitting formula incorporating finite shell thickness is introduced to improve the accuracy of modeling bubble acceleration in the late nonlinear stage, providing better predictions for actual target designs. Collectively, these findings deepen the mechanistic understanding of ablative instability evolution from linear to deeply nonlinear regimes, and offer both theoretical guidance and practical strategies for optimizing high-gain fusion target performance.