Over the past two decades, studies about the spectral invariant theory have been developed rapidly in vegetation remote sensing. The theory has been widely used in vegetation parameter measurement, canopy reflectance modeling, and biophysical parameters retrieval. A review paper titled "Photon recollision probability and the spectral invariant theory: Principles, methods, and applications" was published by the author in “Remote Sensing of Environment” in 2023 （DOI: 10.1016/j.rse.2023.113859）. The current paper provides a comprehensive overview of the background of spectral invariant theory, general principles of the theory, determination and applications of spectral invariants. Recent progresses of the theory are summarized and potential future developments are discussed. A special section is dedicated to the researches made by Chinese scholars. The goal is to provide a synthetic overview of the theory. Some new thoughts about the theory are also given in the paper.（1） The spectral invariant theory evolves from the successive orders of scattering approximation method of the multiple scattering process of photons in vegetation canopy. The theory faciliates the conversion of spectral parameters between different spectral bands and different scales （mainly between leaves and canopy） and provides new means for calculating the directional reflectance, albedo, and fluorescence escape probability.（2） Spectral invariants can be obtained through empirical methods, spectral methods, and structural methods. The spectral method is divided into single scale spectral method and spectral scaling method, and the structural method is divided into the Silhouette to Total Area Ratio （STAR） method, clumping index method, Stenberg method, and approximation method. Different methods can be cross-validated.（3） The spectral invariant theory has been applied in a number of canopy reflectance models. Based on these models, researchers have carried out a large number of inversion studies for vegetation structural parameters and physiological parameters. The principles, methods and applications of the theory can be further explored in the future.（4） New approximation methods for the spectral invariants are proposed and new formulae for the visible sunlit leaf area index and the hemispherical directional area scattering factor are summarized. Chinese researchers have made significant contribution to the development of the theory, especially in calculating the escape probability of the solar induced fluorescence using the theory.