As a new type of cooling technology, radiative cooling achieves temperature reduction through spectral regulation. Compared with the traditional active cooling technologies such as absorption-based cooling and compression-based cooling, the radiative cooling offers unique advantages, which are of great significance in environmental protection and energy utilization. First of all, the basic principle of radiative cooling and the radiative cooling within the natural biological systems are introduced in this review. The biological systems achieve their regulations of radiative cooling through controlling the materials, microstructures and behaviors in the systems, which also provide inspiration for us to explore new radiative cooling materials and devices. We also summarize the various mechanisms of radiative cooling in the biological systems and the optimization of such cooling structures. The recent research progress of bio-inspired radiative cooling is also presented. At the end, the outlook of the research directions, potential applications, and the material fabrication approaches for bio-inspired radiative cooling are discussed. The radiative cooling materials and devices with high power output and intelligent control should be an important development direction of bio-inspired radiative cooling in the future. With the integration of advanced micro/nano fabrication technology, bio-inspired radiative cooling will have a broader market and much room of applications in the future.