The development of unmanned aerial vehicles (UAVs) has become a revolution in the fields of data collection, surveying, monitoring, and tracking objects in the field. Many control and navigation algorithms are experimented and deployed for UAVs, especially quadrotors. Recent numerous approaches are geared towards reducing the influence of external disturbances to enhance the performance of UAVs. Nevertheless, designing cutting-edge controllers following the requirements of the applications is still a huge challenge. Based on the operating characteristics and movement principle of a quadrotor, this work reviews potential control algorithms of the current researches in the field of the quadrotor flight controller. Besides, a comparison has been made to provide an overview of the advantages and disadvantages of the mentioned methods. At last, the challenges and future directions of the quadrotor flight controller are suggested.