A summary of the current status of concrete dams impacted by leakage dissolution is provided. In view of material science, the leakage dissolution process and the degradation of mechanical properties of concrete in hydraulic structures are reviewed based on results of experimental and theoretical research. In view of engineering structures, the spatial evolution law of mechanical properties of concrete for dam bodies impacted by leakage dissolution is summarized. Furthermore, the spatial variability of physical and mechanical parameters of concrete dams is analyzed, and advances in the random field model for description of the spatial variability of dam body mechanical performance and the random finite element method for evaluation of dam body dynamic performance are discussed. Finally, three important topics for further research, including the mechanism of leakage dissolution causing damage to concrete structures under multiple environmental and load factors, the spatial random field model for description of the mechanical performance of concrete dams impacted by leakage dissolution, and the seismic safety analysis method for assessment of the dynamic performance of aged concrete dams under the influence of leakage dissolution, are proposed.