Spectral detection technology has a wide range of applications in biomedicine, national defense, security check, production monitoring, geological survey, material analysis, environmental protection, disaster reduction and so on. However, due to the existing detectors and application technology conditions, the flexibility and applicability of traditional spectral instruments is limited in above territories. The miniaturization and integration of spectral systems is one of the inevitable development trends. With the critical demand of miniaturized, chip and intelligent spectral imaging and the maturation of the computational spectral imaging theory, computational spectrometers have attracted much attention because of the ability to improve spectral resolution while reducing the mass and volume of devices or systems. The computational spectrometers based on compressed sensing theory have the advantages of short calculation time, wide application range, flexible structure, low cost and so on. This review compares the design methods of various spectral structure based on the framework of compressed sensing theory, analyzes the compression spectral measurement technology which realizes the direct coding of spectrum domain and reveals the development trend and bottleneck of miniaturized, intelligent chip spectrometers based on compressed sensing algorithm.