Fiber-reinforced composites have become the preferred material in the fields of aviation and aerospace because of their high-strength performance in unit weight. The composite components are manufactured by near net-shape and only require finishing operations to achieve final dimensional and assembly tolerances. Milling and grinding arise as the preferred choices because of their precision processing. Nevertheless, given their laminated, anisotropic, and heterogeneous nature, these materials are considered difficult-to-machine. As undesirable results and challenging breakthroughs, the surface damage and integrity of these materials is a research hotspot with important engineering significance. This review summarizes an up-to-date progress of the damage formation mechanisms and suppression strategies in milling and grinding for the fiber-reinforced composites reported in the literature. First, the formation mechanisms of milling damage, including delamination, burr, and tear, are analyzed. Second, the grinding mechanisms, covering material removal mechanism, thermal mechanical behavior, surface integrity, and damage, are discussed. Third, suppression strategies are reviewed systematically from the aspects of advanced cutting tools and technologies, including ultrasonic vibration-assisted machining, cryogenic cooling, minimum quantity lubrication (MQL), and tool optimization design. Ultrasonic vibration shows the greatest advantage of restraining machining force, which can be reduced by approximately 60% compared with conventional machining. Cryogenic cooling is the most effective method to reduce temperature with a maximum reduction of approximately 60%. MQL shows its advantages in terms of reducing friction coefficient, force, temperature, and tool wear. Finally, research gaps and future exploration directions are prospected, giving researchers opportunity to deepen specific aspects and explore new area for achieving high precision surface machining of fiber-reinforced composites.