The operational modal analysis (OMA), as a passive technique, has found a practical application in the structural health monitoring (SHM) of structures in service subjected to dynamic loadings. The state of structural integrity is judged by exploring the changes in values of the modal parameters estimated by the OMA. However, the entire framework of on-line damage identification and continuous monitoring is rather complex, involving several key building blocks. This work reviews the main steps in achieving the functionality of automatic damage identification in composite structures with a particular focus on wind turbine blades. The sensor instrumentation, extraction of damage-sensitive features from measured response signals, removal of environmental influence, automatic classification of physical and spurious modes of the system, and application of a statistical control to obtain the information on the possible structural damage are discussed. The merits and limitations of the OMA-based SHM approach for composite wind turbine blades are indicated.