Composite materials are steadily replacing traditional materials in a wide range of industry sectors thanks to their remarkable properties. Damage in composite materials exhibits complex failure modes which are difficult to identify by conventional techniques. Composite materials demonstrate complex nonlinear vibration behaviour where conventional vibration-based structural health monitoring (VSHM) methods might not give adequate information for damage identification. This thesis investigates the capabilities of singular spectrum analysis (SSA) as a technique for developing a completely data-based VSHM methodology. The methodology decomposes the vibration responses in a certain number of principal components having in consideration all rotational patterns at any frequency including the nonlinear oscillations. This thesis develops two approaches to use SSA in the time and frequency domain. The methodology has been validated using a numerical system and an experiment with delaminated beams. The results demonstrate the methodology capability for assessing damages at different locations and with different sizes. The progression of damage can also be tracked. Delamination was successfully assessed in composite laminated plates with different delamination locations, in-plane and through different layers. Damage in wind turbine blades was assessed by the damage assessment methodology with a statistical hypothesis inspection phase based on probability distribution functions. Different damage locations and sizes were assessed as well as damage progression. This thesis explores the use of smart materials which enable self-sensing and self-diagnosing of its structural integrity coupled with the data-based VSHM. The results demonstrate the substantial potential of this approach. Overall, the data-based VSHM methodology presented in this thesis is proven to give adequate information about the presence, location and extent of delamination and other defects in different composite laminated structures.