Optical spectrometers have become an indispensable tool in various fields that involve optical spectrum analysis. Its application ranges in many areas, such as biochemical sensing, food and drug testing, medical treatment and environmental monitoring. The application of traditional spectrometers is greatly limited due to the size, high power consumption and price, difficult secondary development. With the development of micro processing, miniaturized spectrometers have been developed. Compared to the traditional spectrometers, miniaturized spectrometers have the advantages of low cost, small volume, low power consumption and easy secondary development, which expands the application. However, miniaturized spectrometer, which is usually based on discrete optical components, doesn’t have high integration and flexibility. As the requirement of portability becomes higher and higher, further miniaturization and integration has become a trend of spectrometer. On-chip spectrometers, with apparent Size, Weight, and Power (SWaP) advantages, have unprecedented impact on applications ranging from unmanned devices to intelligent platform. Among the methods to realize on-chip spectrometers, silicon photonics offers an approach to realize an integrated and cheap spectroscopic system because of its mature processing and integration. During the last few years, on-chip spectrometers have become an enormously active area, resulting in significant progress. In this review, it summarizes the principle of the silicon based on-chip spectrometer, and introduces the developments of the dispersive spectrometers including spectrometers based on the etch diffraction grating, arrayed waveguide grating and multimode waveguides, and Fourier transform spectrometers including spatial heterodyne, stationary wave, thermos-optic, digital and MEMS Fourier transform spectrometers. We analyze the characteristics and applications of these spectrometers. Our research has also been demonstrated. By combining the mach-zehnder interferometer spectrometer and the arrayed waveguide grating spectrometer, the large spectral range and high resolution have been simultaneously achieved. At the end, we also discuss the future challenges and prospects in this field, which can give some reference for the research of on-chip spectrometers.