Nature-inspired self-cleaning surfaces have attracted considerable attention from both fundamental research and practical applications. This review adopts a chemical-engineering point of view and focuses on mechanisms, modelling, and manufacturing (M3) of nature-inspired self-cleaning surfaces. We will introduce six nature-inspired self-cleaning mechanisms: The Lotus-effect, superhydrophobic-induced droplet jumping, superhydrophobic-induced unidirectional movement of water droplet, underwater-superoleophobic-based self-cleaning, slippery-based self-cleaning, and dry self-cleaning. These mechanisms of nature self-cleaning examples are popular and well-known as well as have been widely applied or exhibited potential applications in our daily life and industrial productions. The mathematical and numerical modelling of the identified self-cleaning mechanisms will be carefully introduced, which will contribute to the rational design and reproducible construction of these functional self-cleaning surfaces. Finally, we will discuss how these materials can be produced, with a focus on scalable manufacturing. We hope this review will strengthen the understanding on nature-inspired self-cleaning surfaces and stimulate interdisciplinary collaboration of material science, biology and engineering.