The research background, design scheme, and structure characteristics of a convex grating imaging spectrometer based on a concentric structure are introduced. Five main configuration types of concentric imaging spectrometers with a convex grating at home and abroad are reviewed, including Offner type, off-plane type, catadioptric type, +1st order diffraction type, and freeform surface type. The advantages and disadvantages of these five configuration types are summarized. It has important guiding significance for the research and development of a new generation of light and small imaging spectrometers with high imaging quality, high resolution, high diffraction efficiency, large relative aperture, long slit, and wide wavelength range.