The automotive industry is developing in the direction of intelligence and connectivity, and the emergence of connected and automated vehicles(CAVs) enables traffic managers to find a solution to alleviate traffic congestion, improve road safety and reduce energy consumption. Therefore, this paper investigates the latest achievements in the fields of mixed traffic flow models, cooperative control of CAVs and traffic management. And the research status and progress of intelligent transportation systems in terms of vehicle-road-cloud integration is systematically elaborated. First, the framework of mixed traffic systems based on vehicle-road-cloud integration is analyzed, and the composition and function of each part are sorted out. Second, the modelling methods of mixed traffic flow are summarized. And, the nature of traffic phenomena is explored. In addition, the characteristics, advantages and limitations of various methods are proposed. Then, the optimal control of mixed traffic system is discussed. Moreover, the potential of intelligent and connected traffic around four aspects of traffic flow, namely, stability, safety, efficiency and green transportation is detailed. The control plants and objectives in different traffic scenarios are sorted out, and the instructive control methods are summarized. Finally, the problems and challenges of vehicle-road-cloud integration are presented, and the future research directions are highlighted.