Recent developments in computer and communication technologies are leading to an increasingly networked and wireless world. This raises new challenging questions in the context of networked control systems, especially when the computation, communication, and energy resources of the system are limited. To efficiently use the available resources, it is desirable to limit the control actions to instances when the system really needs attention. Unfortunately, the classical time-triggered control paradigm is based on performing sensing and actuation actions periodically in time (irrespective of the state of the system) rather than when the system needs attention. Therefore, it is of interest to consider event-triggered control (ETC) as an alternative paradigm as it is more natural to trigger control actions based on the system state, output, or other available information. ETC can thus be seen as the introduction of feedback in the sensing, communication, and actuation processes. To facilitate an easy implementation of ETC, we propose to combine the principles and particularly the benefits of ETC and classical periodic time-triggered control. The idea is to periodically evaluate the triggering condition and to decide, at every sampling instant, whether the feedback loop needs to be closed. This leads to the periodic event-triggered control (PETC) systems. In this chapter, we discuss PETC strategies, their benefits, and two analysis and design frameworks for linear and nonlinear plants, respectively.