Abstract: A variety of high-energy radiations in the space radiation environment, including Galactic Cosmic Rays (GCRs), Solar Particle Event (SPEs), and secondary neutrons, can induce diverse space radiation effects on DNA structure of astronauts and precision electronic equipment, posing a serious threat to the health of astronauts and the normal operation of devices. At present, developing composite materials with both high-efficiency radiation shielding properties and excellent overall performance is one of the most effective protection approaches. This study systematically elaborates on the radiation hazards and shielding mechanisms of GCRs, SPEs, X-rays, γ-rays, and neutrons, and then reviews the research progress of various composite materials, including metal matrix, polyethylene (PE) matrix, polybenzoxazine matrix, polyether ether ketone (PEEK) matrix, and polyvinyl alcohol (PVA) matrix composites. The mechanisms by which fillers influence the key properties of matrix materials are discussed in detail. Finally, the design strategies and development trends of radiation shielding composites in the future are outlined.