Advanced composites are being increasingly used in state-of-the-art aircraft and aerospace structures. In spite of their many advantages composite materials are highly susceptible to hidden flaws that may occur at any time during the life of a structure and if undetected, may cause sudden and catastrophic failure of the entire structure. An example of such a structural component is the "honeycomb composite" in which thin composite skins are bonded with adhesives to the two faces of extremely lightweight and relatively thick metallic honeycombs. These components are often used in aircraft and aerospace structures due to their high strength to weight ratio. Unfortunately, the bond between the honeycomb and the skin may degrade with age and service loads can lead to separation of the load-bearing skin from the honeycomb (called "disbonds") and compromise the safety of the structure. The need for model-based studies is widely recognized in the NDE community and a great deal of work has indeed been carried out for simple, metallic structures. However the literature on composite structures is rather limited due to the enormous mathematical complexity involved in dealing with them. In this dissertation a comprehensive approach including numerical (finite element method) and analytical method is used for calculating the ultrasonic wavefield in composite structural components with and without defects. Laboratory experiments are carried out on a composite honeycomb specimen containing damage to the skin or a localized disbond at the skin-core interfaces. The skin and the honeycomb composite are considered separately in order to understand the interaction of ultrasonic waves with damage in the two structures. The waves are launched into the specimen using a broadband PZT transducer and are detected by a distributed array of identical transducers located on the surface of the specimen. The guided wave components of the signals are shown to be strongly influenced by the presence of a defect in the skin or the honeycomb composite structure. The experimentally observed results are used to develop an autonomous scheme to locate the disbonds. The calculated results from the simulations are compared with existing and new experiments to validate and improve the models. The results should be very useful in model-based understanding of ultrasonic data collected during nondestructive inspection and evaluation (NDI/NDE) of advanced aircraft and aerospace structure and in the development of reliable health monitoring systems in the structures.