This paper introduces event-triggered and self-triggered control systems, which are designed to limit sensor and control computation and communication to instances when the system needs attention. Event-triggered control is reactive, performing sensing and actuation when the plant state deviates from a desired value, while self-triggered control is proactive, computing the next sampling or actuation instance in advance. The paper discusses the differences between state feedback and output feedback for event-triggered control and explores how these control strategies can be implemented using existing wireless communication technology. It also presents applications of event- and self-triggered control in wireless control systems, particularly in process industries. The paper covers the basics of these control strategies, including the use of Lyapunov functions to ensure stability and performance, and provides examples and numerical results to illustrate the concepts. Additionally, it discusses the challenges and advantages of event-triggered and self-triggered control in the context of energy, computation, and communication constraints.This paper introduces event-triggered and self-triggered control systems, which are designed to limit sensor and control computation and communication to instances when the system needs attention. Event-triggered control is reactive, performing sensing and actuation when the plant state deviates from a desired value, while self-triggered control is proactive, computing the next sampling or actuation instance in advance. The paper discusses the differences between state feedback and output feedback for event-triggered control and explores how these control strategies can be implemented using existing wireless communication technology. It also presents applications of event- and self-triggered control in wireless control systems, particularly in process industries. The paper covers the basics of these control strategies, including the use of Lyapunov functions to ensure stability and performance, and provides examples and numerical results to illustrate the concepts. Additionally, it discusses the challenges and advantages of event-triggered and self-triggered control in the context of energy, computation, and communication constraints.