<p>The rapid advancement of Connected and Autonomous Vehicle (CAV) technology has driven research into innovative optimization strategies for enhancing the efficiency and safety of CAVs. This paper systematically reviews the current state of optimization approaches for managing CAVs in mixed-traffic environments and classifies them based on the investigated problem. It begins with an examination of CAV management at unsignalized intersections, focusing on trajectory planning, conflict resolution, and energy efficiency. While significant progress has been made, extending these methods to multiple multi-lane intersections, considering lane changes, market penetration, and communication quality remains a critical research need. The paper also explores platooning optimization on highways and near intersections, emphasizing the role of lane-changing models in maximizing capacity in mixed traffic. Additionally, real-time data integration and calibration in mixed-traffic connected environments are identified as crucial for future advancements. The study examines various optimization-based strategies, such as autonomous mobility on-demand services and dynamic lane reversal, and their implications for traffic flow and capacity. Finally, it highlights the transformative potential of artificial intelligence, including reinforcement learning and deep learning techniques, in optimizing CAV fleet and traffic management strategies. Overall, this study provides a comprehensive overview of current research and outlines critical directions for future advancements in CAV traffic and fleet management.</p>