In the past decades, Lamb waves (LW) have seen encouraging results when applied to non destructive testing (NDT) and structural health monitoring (SHM), with important research done continuously through the years in both fields. This paper is a comprehensive review on equipment, testing procedures and techniques adopted in NDT and SHM, with emphasis in applications involving SHM of adhesive joints. The fundamentals of LW and their application to damage detection are discussed, and different signal processing, statistical, machine learning and simulation methods are presented. The paper represents a basis to deepen the understanding about the problem at hand and is a thorough compilation of relevant information to future work. Although LW-based SHM methods have been heavily studied, there is a gap of few to no studies between these topics and adhesive joints, namely, for monitoring weak adhesion.