In recent years, the safety of oil and gas pipelines has become a primary concern for the pipeline industry. This paper presents a comprehensive study of the vulnerability concepts that may be used to measure the safety status of pipeline systems. The origins of the vulnerability concepts are identified, the development and evolution of the vulnerability concepts are described, and the main connotations of the four levels of vulnerability concepts applied in different fields at this stage are summarized. Qualitative and quantitative methods of vulnerability assessment are comprehensively investigated, and the advantages and disadvantages, scope of application and key issues faced are compared and summarized. The research and analysis show that the vulnerability assessment of oil and gas pipelines is at a preliminary stage, and there is an urgent demand to establish a unified vulnerability concept and assessment system for oil and gas pipeline systems. The current qualitative or semi-quantitative assessment of pipeline vulnerability research lacks reasonable and scientific standards and bases for the classification of indicators and the determination of indicator scores, and it needs to focus on the establishment and improvement of quantitative assessment models.