The damage behavior and performance prediction of fiber-reinforced composite materials under low-velocity impact have attracted considerable attention in the aerospace field. This paper reviews the research progress in low-velocity impact studies of composites, covering experimental investigations, theoretical modeling, numerical simulation, and machine learning-based modeling approaches. Focusing on single-factor and multi-factor coupling effects, the review summarized the damage mechanisms and evolution characteristics of composite laminates under low-velocity impact, and clarifies typical failure modes and their coupling mechanisms. By integrating single and repeated impact scenarios, it outlined the advancements in numerical simulation concerning strain-rate effects, delamination, internal damage evolution, and multi-scale analysis strategies. In the realm of theoretical modeling, the applications and extensions of energy-balance models and spring-mass models in impact response and damage prediction were analyzed. Additionally, the applications of machine learning methods in impact damage identification, parameter optimization, and performance prediction were summarized. Future research should prioritize the construction of high-fidelity experimental databases, the development of multi-physics coupled models, the integration of physics-informed machine learning methods, and the promotion of deep integration among experimental, theoretical, simulation, and intelligent modeling approaches, to achieve a leap-forward development in the low-velocity impact behavior of composite materials from mechanistic cognition to predictive control.