The term Cyber-Physical Systems (CPS) typically refers to engineered, physical and biological systems monitored and/or controlled by an embedded computational core. The behaviour of a CPS over time is generally characterised by the evolution of physical quantities, and discrete software and hardware states. In general, these can be mathematically modelled by the evolution of continuous state variables for the physical components interleaved with discrete events. Despite large effort and progress in the exhaustive verification of such hybrid systems, the complexity of CPS models limits formal verification of safety of their behaviour only to small instances. An alternative approach, closer to the practice of simulation and testing, is to monitor and to predict CPS behaviours at simulation-time or at runtime. In this chapter, we summarise the state-of-the-art techniques for qualitative and quantitative monitoring of CPS behaviours. We present an overview of some of the important applications and, finally, we describe the tools supporting CPS monitoring and compare their main features.