Urban intersections are critical areas where traffic flows converge and conflict, significantly influencing traffic safety, economic benefits, and energy consumption. Effective management and control of intersections have become a central focus in transportation research. With the advancement of automation technology, intersection management methods combined with connected autonomous vehicles (CAVs) have been rapidly developed. However, a comprehensive analysis of these emerging approaches remains lacking, from intersection design to management. This paper systematically reviews recent research on cooperative intersection management (CIM). Firstly, it explores the design of intersections. Secondly, various management objectives and evaluation methods are outlined. Thirdly, relevant research on vehicle trajectory control at the micro level, intersection management at the meso level, and arterial traffic flow regulation and network management at the macro level are discussed in detail. Based on this analysis, this paper identifies future research themes, emphasizing the need for trade-offs, integration, and coordination. Key areas for further study include enhancing the alignment between abstract models and real-world applications, balancing the performance of control methods with their implementation efficiency, and integrating various intersection control strategies to collectively enhance traffic efficiency, sustainability, and safety cooperatively.