Different methods are commonly used for non-destructive testing in structures; among others, acoustic emission and ultrasonic inspections are widely used to assess structures. The research presented in this paper is motivated by the need to improve the inspection capabilities and reliability of structural health monitoring (SHM) systems based on ultrasonic guided waves with focus on the acoustic emission and acousto-ultrasonics techniques. The use of a guided wave based approach is driven by the fact that these waves are able to propagate over relatively long distances, and interact sensitively and uniquely with different types of defect. Special attention is paid here to the development of efficient SHM methodologies. This requires robust signal processing techniques for the correct interpretation of the complex ultrasonic waves. Therefore, a variety of existing algorithms for signal processing and pattern recognition are evaluated and integrated into the different proposed methodologies. As a contribution to solve the problem, this paper presents results in damage detection and classification using a methodology based on hierarchical nonlinear principal component analysis, square prediction measurements and self-organizing maps, which are applied to data from acoustic emission tests and acousto-ultrasonic inspections. At the end, the efficiency of these methodologies is experimentally evaluated in diverse anisotropic composite structures.