The Lamb wave based, non-contact damage detection techniques are developed using the Modified Time Reversal (MTR) method and the model based inverse problem approach. In the first part of this work, the Lamb wave-based MTR method along with the non-contacting sensors is used for structural damage detection. The use of non-contact measurements for MTR method is validated through experimental results and finite element simulations. A novel technique in frequency-time domain is developed to detect linear damages using the MTR method. The technique is highly suitable for the detection of damages in large metallic structures, even when the damage is superficial, and the severity is low. In this technique, no baseline data are used, and all the wave motion measurements are made remotely using a laser vibrometer. Additionally, this novel MTR based technique is not affected due to changes in the material properties of a structure, environmental conditions, or structural loading conditions. Further, the MTR method is improved for two-dimensional damage imaging. The damage imaging technique is successfully tested through experimental results and finite element simulations. In the second part of this work, an inverse problem approach is developed for the detection and estimation of major damage types experienced in adhesive joints. The inverse problem solution is obtained through an optimization algorithm wherein the objective function is formulated using the Lamb wave propagation data. The technique is successfully used for the detection/estimation of cohesive damages, micro-voids, debonds, and weak bonds. Further, the inverse problem solution is separately obtained through a fully connected artificial neural network. The neural network is trained using the Lamb wave propagation data generated from Wavelet Spectral Finite Element (WSFE) model which is computationally much faster than a conventional finite element model. This inverse problem approach technique requires a single point measurement for the inspection of the entire width of the adhesive joint. The proposed technique can be used as an automated quality assurance tool during the manufacturing process, and as an inspection tool during the operational life of adhesively bonded structures.