As a special kind of linear systems, isotropic linear systems not only have a wide range of engineering application background, but also have many special properties that are not available in general linear systems. In this paper, the characteristics of isotropic linear systems are systematically summarized, especially the relationship between the isotropic linear systems and their corresponding complex coefficient linear systems. In addition, the necessity of designing isotropic feedback for isotropic linear systems is also discussed, and the spacecraft attitude control system is introduced as a specific application example of isotropic linear systems. Combining several common types of engineering control systems that can be described by isotropic linear systems, the study status and existing results of isotropic linear systems are briefly summarized and discussed. Further research directions are briefly introduced at the end of this paper.