Networked control systems (NCSs) are systems whose control loops are closed through communication networks such that both control signals and feedback signals can be exchanged among system components (sensors, controllers, actuators, and so on). NCSs have a broad range of applications in areas such as industrial control and signal processing. This survey provides an overview on the theoretical development of NCSs. In-depth analysis and discussion is made on sampled-data control, networked control, and event-triggered control. More specifically, existing research methods on NCSs are summarized. Furthermore, as an active research topic, network-based filtering is reviewed briefly. Finally, some challenging problems are presented to direct the future research.