Predictive control encompasses a family of controllers that continually replan the system inputs during a certain time horizon to optimize their expected evolution according to a given criterion. This methodology has among its current challenges the adaptation to the paradigm of the so-called cyber-physical systems, which are composed of computers, sensors, actuators and physical entities of various kinds, including robots and even human beings who exchange information to control physical processes. This tutorial introduces the core concepts for the application of predictive control to cyber-physical systems by reviewing a series of examples that exploit the versatility of this design framework so as to solve the challenges presented by 21st century applications.