Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial control processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. In this paper: i) we propose a mathematical framework for cyber-physical systems, attacks, and monitors; ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and ii) we design centralized and distributed attack detection and identification monitors. Finally, we validate our findings through compelling examples.