The information society has higher and higher requirements for the collection, transmission and storage of digital signals, and signal utilization efficiency has become an increasingly important part of the digital signal processing process. The traditional digital signal processing needs to satisfy the Nyquist sampling theorem to ensure the restoration of the signal, while the digital signal processing method based on compressed sensing can sample and reconstruct the signal under the conditions that much lower than the Nyquist sampling theorem. Undoubtedly, the utilization efficiency of digital signals has been greatly accelerated. In this article, taking hyperspectral images and videos as examples, we review the basic theory, reconstruction model, and reconstruction algorithm of 3D data compressed sensing. We analyze, summarize, and discuss the existing literature. Finally, the research status of compressive sensing reconstruction methods for hyperspectral images and videos is compared, and several important research directions for compressive sensing reconstruction of 3D data in the future are proposed.