Abstract: Multi-agent collaborative control refers to multiple intelligent agents with autonomous perception, decision-making, and execution capabilities, which work together through inter-agent cooperation to achieve common goals (usually complex tasks that cannot be independently accomplished by a single agent). Such systems typically exhibit high robustness and fault tolerance, and can promote knowledge sharing and learning among the systems, thereby effectively reducing costs and resource consumption. With the rapid advancement of technology, multi-agent collaborative control has demonstrated strong application potential in various fields in recent years. For instance, it has been widely utilized in industrial manufacturing, transportation, smart grids, unmanned aerial vehicle formations, and other areas. We systematically review the research progress in multi-agent systems control in recent years, and focus on summarizing and generalizing the multi-agent collaborative control problems under finite-time, fixed-time, and predefined-time constraints. Then we deeply compare the control strategies and methods in different control scenarios. Finally, we analyzes the challenges faced by the current field of multi-agent finite-time collaborative control and explores the potential future development directions.