Abstract-Cyber-physical systems are ubiquitous in power systems, transportation networks, industrial processes, and critical infrastructures. These systems need to operate reliably in the face of unforeseen failures and external malicious attacks. This paper summarizes and extends our results on the security of cyber-physical systems based on geometric control theory: (i) we propose a mathematical framework for cyberphysical systems, attacks, and monitors; (ii) we characterize fundamental monitoring limitations from system-theoretic and graph-theoretic perspectives; and (iii) we design centralized and distributed attack detection and identification monitors. Finally, we design an attack strategy for a group of power generators to physically compromise the functionality of other generators. Novel contributions include a more general framework, the design of novel centralized and distributed identification monitors, and the attack design case study.