This dissertation focuses on the detection and localization of damage in plate-like structures using active guided ultrasonic wave inspection common to the research areas of non-destructive evaluation (NDE) and structural health monitoring (SHM). Inspection consists of first interrogating the structure with a narrowband input waveform, exciting multiple plate modes, and then analyzing the resulting damage scattered wave field using a signal processing method (detector) to decide if damage is present or not. The successful application of guided waves in plate structures is unfortunately difficult due to the wave propagation environment being dispersive, multi-modal, and multi-path. This dissertation attempts to reduce these problems and to extend the knowledge in ultrasonic guided wave structural health monitoring (UGWSHM) by : characterizing the wave propagation environment through theoretical modeling of guided wave modes excited via circular piezoelectric transducers, developing signal processing techniques to experimentally estimate dispersion curves in-situ and applying novel statistical signal processing methods to detect and locate damage through multi-mode and multi-frequency array detectors. Experiments are performed on aluminum and carbon fiber laminate plates to identify propagating guided wave modes and to detect and locate damage, validating the proposed models and signal processing methods