The main objective of Structural Health Monitoring (SHM) is to be able to continuously monitor and assess the status of the integrity of a structure or its components with a high level of confidence and reliability. In general, the common techniques employed in SHM for monitoring structures and detecting damages can be divided into two categories: (1) vibration-based approach and (2) wave-based approach. Since wave-based approach can provide better local health status information and has higher sensitivity to damages than vibration-based approach, this thesis focuses on damage localization of plate structure using wave-based approach by first characterizing elastic waves in composite laminates; then using a time-frequency signal processing technique to analyze dispersive stress waves; and lastly a least-squares technique is proposed for damage localization. Exact solutions of dispersive relations in a composite lamina and composite laminate are first deduced from three-dimensional (3-D) elasticity theory. The dispersion relations containing infinite number of symmetric and antisymmetric wave modes are numerically solved. Then, to make dispersive wave solutions tractable in composites, a higher-order plate theory is proposed. The dispersion relations of three antisymmetric wave modes and five symmetric wave modes can be analytically determined. The dispersion curves of phase velocity and group velocity are obtained from the two theories. From the results of the 3-D elasticity theory and higher-order plate theory, it can be seen from dispersion curves that the higher-order plate theory gives a good agreement in comparison with those obtained from 3-D elasticity theory in the relatively high frequency range; and especially for the lowest symmetric and antisymmetric modes, dispersion relation curves obtained from the two theories match very well. In the Chapter of time-frequency analysis of dispersive waves, a Wavelet Transform (WT) is directly performed on a transient dispersive wave to extract the time-frequency information of transient waves. Consequently, the dispersion relations of group velocity and phase velocity can be mathematically obtained. Experiments are set up to verify the proposed WT method, in which a lead break is used as a simulated acoustic emission source on the surface of an aluminum plate. The dispersion curves of both phase and group velocities of the lowest flexural wave mode obtained from the experiments by using WT show good agreement with theoretical prediction values. Having group velocities verified from the experiments, a least-squares method is proposed to SHM field for iteratively searching damage location based on elastic wave energy measurements. The method is suitable for achieving automated SHM system since the proposed method is based on active damage detection technique and deals with the entire sensor data in the least-squares algorithm without the need of ambiguously measuring the time-of-flights. The simulated data are obtained from finite difference method in conjunction with Mindlin plate theory. Simulated examples for damage detection are demonstrated by using the least-squares method. Moreover, an active SHM system is set up to validate the feasibility of the least-squares damage localization technique. From the simulated and experimental results, it is shown that the estimated damage position by least-squares method gives good agreement with the targeted damage location.