Spectral imaging aims to obtain three-dimensional spatial-spectral data cubes of target scenes that substantially improves the recognition and classification capabilities of targets. It has been widely used in various fields, including military and civilian applications. Traditional spectral imaging techniques are mostly based on the Nyquist sampling theory. However, these techniques face challenges in balancing spatial, spectral, and temporal resolutions due to limitations posed by two-dimensional sensor arrays when capturing three-dimensional data cubes. The computational spectral imaging is based on the compressed sensing theory system. First, the optical system is used to encode and compress the projection of the three-dimensional data cube. Then, a spectral reconstruction algorithm is used to decode the three-dimensional data cube, which can balance spatial, spectral, and temporal resolutions. Starting from the unified theory of computational spectral imaging, this paper systematically summarizes three methods of optical field encoding: image plane, point spread function, and spectral response encoding. Additionally, it explores two types of algorithmic decoding: one is based on physical models and prior knowledge, while the other is based on deep learning for end-to-end reconstruction. Furthermore, this paper discusses the differences and connections between these methods, analyzing their respective advantages and disadvantages. Finally, it explores future development trends and research directions of computational spectral imaging technology.