The Bird-like Flapping-wing Air Vehicle (BFAV) is a robotic innovation that emulates the flight patterns of birds. In comparison to fixed-wing and rotary-wing air vehicles, the BFAV offers superior attributes such as stealth, enhanced maneuverability, strong adaptability, and low noise, which render the BFAV a promising prospect for numerous applications. Consequently, it represents a crucial direction of research in the field of air vehicles for the foreseeable future. However, the flapping-wing vehicle is a nonlinear and unsteady system, posing significant challenges for BFAV to achieve autonomous flying since it is difficult to analyze and characterize using traditional methods and aerodynamics. Hence, flight control as a major key for flapping-wing air vehicles to achieve autonomous flight garners considerable attention from scholars. This paper presents an exposition of the flight principles of BFAV, followed by a comprehensive analysis of various significant factors that impact bird flight. Subsequently, a review of the existing literature on flight control in BFAV is conducted, and the flight control of BFAV is categorized into three distinct components: position control, trajectory tracking control, and formation control. Additionally, the latest advancements in control algorithms for each component are deliberated and analyzed. Ultimately, a projection on forthcoming directions of research is presented.