For multi-agent systems, the problem of distributed feedback optimization is about forcing the output of the multi-agent system to converge to the optimizer of certain global cost function by means of a distributed controller that depends on the local state of each agent, the real-time feedback value of the local gradient information, and the real-time information exchange with other agents. In some special cases, the distributed feedback optimization problem can be reduced to a distributed optimization problem or a centralized feedback optimization problem. This paper reviews the current state of the art of distributed feedback optimization and discusses its outlook. Through literature survey and inductive reasoning, this paper first introduces the research background and significance of distributed feedback optimization and the development status of related fields, then analyzes the fundamental difficulties of distributed feedback optimization, and then summarizes the research status of distributed feedback optimization from the aspects of linear systems and nonlinear systems. Finally, this paper gives the future development direction.