The research topic of the thesis deals with the application of guided and bulk waves to monitor critical engineering structures such as composites and welds, which are commonplace in aeronautics. In the first part of the research, several Structural Health Monitoring (SHM) techniques were proposed and developed using linear and nonlinear damage sensitive features. Furthermore, a novel technique was proposed to select the optimal “damage sensitive” frequency of guided waves in a pitch-catch configuration. The selected frequency was further exploited in order to construct a nonlinear baseline-free imaging technique for visualization of a composite containing a delamination defect using a sparse array of bonded piezo ceramics. The second part of the research addresses the challenging problem of detecting kissing bonds in friction stir welded joints. Two improvements, including the optimization of immersion linear ultrasonic testing and a nonlinear pulse-inversion chirp-coded harmonic imaging technique, are proposed and verified in experiment. The C-scan fingerprints obtained by the linear technique is capable of illuminating all different types of linear root flaws in the friction stir welds. The density of nonlinear defects such as microcracks accompanying zigzag lines can be further evaluated by the nonlinear pulse-inversion technique. Experimental results were conducted on a variety of samples manufactured by The Welding Institute (TWI).