Both fields of chaos control and synchronization and complex network studies are international hotspots. In this dissertation, we did some deep and detailed studies on chaos control and synchronization of nonlinear circuits and complex networks which are two important research subjects in the above two fields. We put forward and discussed several new methods for chaos control and synchronization in several nonlinear circuits and some complex networks.The main contributions of this dissertation are as follows:(1) We studied the chaos control of a n-scroll Chua's circuit in detailed. At first, the unstable fixed points in the circuit are classified into two different types according to the characteristics of the eigenvalues of the linearized matrix at the fixed points. Then, we reviewed a chaos control method of using feedback of a single state variable in a proportional and differential format, which can only stabilize the first type of unstable fixed points and corresponding periodic orbits. For stabilizing the second type of fixed points and corresponding periodic orbits, we proposed two chaos control methods based on low-pass filters. The method 1 is to use a low-pass filter and the method 2 is to use two low-pass filters. The control results with applying the two different control methods to the circuit are compared. Studies show that both the method 1 and the method 2 can stabilize the two types of fixed points and corresponding periodic orbits, but from the point of view of stabilizing the second type of fixed points, the method 2 is superior to the method 1 with regard to the control speed and attraction basins. The studies