In recent years, cyber-physical systems are gaining increasing attention due to their versatility of use in various application fields. Their peculiar characteristic of integration between computational aspects and physical processes determines the necessity of addressing new vulnerabilities and security issues. Attacks launched in the cyber domain can have consequences on the physical components, posing serious risks to industrial and daily life activities, such as transportation systems or healthcare. Cyber-physical systems are composed by a set of interconnected devices that take measurements from the physical world through sensors and aim at processing the measured data for some purpose. This thesis examines the problem of estimating the state of cyber-physical systems subjected to sensor attacks, known as secure state estimation, starting with a mathematical analysis of the problem based on the existing literature.