The modeling and control of quadrotor UAV-slung load system is a popular research field in recent years. Quadrotor UAV-slung load system is an underactuated nonlinear system formed by connecting the load and the Quadrotor UAV with a cable. The modeling of full state system is usually based on Euler-Lagrange equation. To make convenience for controller design, equivalent transformations and simplifications of the system model are usually adopted. According to the different simplified models, many control methods, such as PD control, feedback linearization and backstepping, are adopted, and has achieved control objectives like UAV trajectory tracking, load trajectory tracking, UAV formation planning and obstacle avoidance, etc. If there exist unmodeled dynamics or unknown parameters in system model, the controller can be improved by adaptive control method or introducing observer, etc. For the sake of enhancing robustness and flight safety, the controller can be developed based on optimum control theory, and the control performance can be further enhanced by use of input shaper and saturation function, etc. Intelligent control methods have achieved initial results in some complex control problems such as UAV path planning. Cooperative transportation by multiple UAVs is another emerging research subproject.