Different from the traditional point-to-point mapping imaging method, computational optical imaging combines the physical regulation of the front-end optical signal with the processing of the back-end digital signal to make the image information acquisition more efficient. This new imaging mechanism is expected to alleviate the contradiction between low manufacturing cost and high performance indicators under the framework of traditional imaging technology, especially in the acquisition of high-dimensional image information. Since the system architecture supported by physical devices is the cornerstone of computational optical imaging, aiming at the sub-technical field of compressive spectral imaging, in this paper, we introduce the existing optical devices that can realize spatial or spectral modulation. Based on this, the architecture of multi-type compressive spectral imaging system is sorted out and summarized, which can be categorized as single-pixel spectral imaging, coded aperture spectral imaging, spatial-spectral dual-coded spectral imaging, microarray spectral imaging and scattering medium spectral imaging, based on the information modulation process. We focus on the information modulation and acquisition principles of various system architectures and their modulation effects on the spatial-spectral data cube, and then analyze and explore the common issues. Finally, the technical challenges faced are given, and the future development trend is discussed.