The industrial and technological sectors are pushing the boundaries to develop a new class of high-pressure vessels for hydrogen storage that aim to improve durability and and endure harsh operating conditions. This review serves as a strategic foundation for the integration of hydrogen tanks into transport applications while also proposing innovative approaches to designing high-performance composite tanks. The goal is to offer optimized, safe, and cost-effective solutions for the next generation of high-pressure vessels, contributing significantly to energy security through technological advancements. Additionally, the review deepens our understanding of the relationship between microscopic failure mechanisms and the initial failure of reinforced composites. The investigation will focus on the behavior and damaging processes of composite overwrapped pressure vessels (COPVs). Moreover, the review summarizes relevant simulation models in conjunction with experimental work to predict the burst pressure and to continuously monitor the degree of structural weakening and fatigue lifetime of COPVs. Simultaneously, understanding the adverse effects of in-service applications is vital for maintaining structural health during the operational life cycle.