Using remote non-destructive techniques, this book aims to estimate the mechanical health condition of a structure that allows to reduce maintenance costs and to ensure safety. The structural health monitoring can be performed through vibration responses measured by sensors instrumented in the structure. Then changes in the dynamical behaviour of the system are identified through the development of identification and detection techniques. Damage or nonlinearity onset is considered responsible for the changes. The identification of damages and nonlinearity onset is always based on the comparison between a current and the reference (normal) states. The robustness of the methods is illustrated on a clamped beam structure with a geometrical nonlinearity at the end. Other examples are considered such as an aircraft mock-up with different levels of damage, some industrial applications and real-life structures.