Convex blazed gratings, which can effectively broaden the spectral range and improve spectral resolution, have gradually evolved into a crucial optical component for lightweight and compact imaging spectroscopy instruments. Their design, processing, and testing involve multidisciplinary interdisciplinary scientific issues, and they continue to be a major area of research in imaging optics applications. This paper summarizes the effects of various grating groove shapes and structural parameters on the spectral range and diffraction efficiency of convex blazed gratings, after providing a brief introduction to the typical functions and applications of convex blazed gratings. Firstly, the latest progress in typical processing methods for convex blazed gratings is reviewed. It focuses on the current fabrication processes and reviews their capabilities in creating convex blazed gratings from three main types of technologies, namely ultra-precision machining, high-energy density beam processing, and chemically assisted fabrication processes. Secondly, the adaptability of the manufacturing process for convex blazed gratings on different scales is summarized, analyzing the adaptation of current procedures to various grating fabrication scales and their bottlenecks. Finally, the characterization methods and future feasible characterization methods for convex blazed gratings are reviewed. The development trend of efficient and precise preparation of convex blazed gratings is pointed out.