In recent years, there has been a significant increase in research on hydrogen due to the urgent need to move away from carbon-intensive energy sources. This transition highlights the critical role of hydrogen storage technology, where hydrogen tanks are crucial for achieving cleaner energy solutions. This paper aims to provide a general overview of hydrogen treatment from a mechanical viewpoint, and to create a comprehensive review that integrates the concepts of hydrogen safety and storage. This study explores the potential of hydrogen applications as a clean energy alternative and their role in various sectors, including industry, automotive, aerospace, and marine fields. The review also discusses design technologies, safety measures, material improvements, social impacts, and the regulatory landscape of hydrogen storage tanks and safety technology. This work provides a historical literature review up to 2014 and a systematic literature review from 2014 to the present to fill the gap between hydrogen storage and safety. In particular, a fundamental feature of this work is leveraging systematic procedural techniques for performing an unbiased review study to offer a detailed analysis of contemporary advancements. This innovative approach differs significantly from conventional review methods, since it involves a replicable, scientific, and transparent process, which culminates in minimizing bias and allows for highlighting the fundamental issues about the topics of interest and the main conclusions of the experts in the field of reference. The systematic approach employed in the paper was used to analyze 55 scientific articles, resulting in the identification of six primary categories. The key findings of this review work underline the need for improved materials, enhanced safety protocols, and robust infrastructure to support hydrogen adoption. More importantly, one of the fundamental results of the present review analysis is pinpointing the central role that composite materials will play during the transition toward hydrogen applications based on thin-walled industrial vessels. Future research directions are also proposed in the paper, thereby emphasizing the importance of interdisciplinary collaboration to overcome existing challenges and facilitate the safe and efficient use of hydrogen.