Systems models are the mainstream paradigm of accident models. STAMP is one of the most popular systems models, which has been applied in most industries. Therefore, the development process of STAMP and its applications and extensions research should be reviewed to reveal the state-of-the-art advances and illustrate further the future research trends and practical applications. According to the PRISMA guidelines, a total of 121 documents are included in this review through screening and exclusion. The development process, from STAMP to STPA and CAST, has achieved the evolution from model to method, which means STAMP has a more robust capacity for conducting accident analysis and engineering safety system. The existing literature involving STAMP mainly focuses on three topics: applications of STAMP and STAMP-based methods (approximately 64%), extensions of STAMP and STAMP-based methods (approximately 22%), and the comparisons with other models/methods (approximately 7%). In recent years, STAMP has been extended through considering the combination with other models/approaches, organisational failures, human factors, integration with Petri net, quantitative analysis, physical process, and the interactions between non-adjacent levels. The following issues may be the research directions in the future. First, adding quantitative analysis to STAMP; second, integrating organisational and human factors into STAMP control structure/flaws classification versa or vice; third, paying more attention to the interactions across levels and within the parallel level. Furthermore, based on STAMP, more techniques and tools can be constructed, and more applications and extensions/improvements will be created in the future.