Enterprise financial risk analysis aims at predicting the enterprises' future financial risk.Due to the wide application, enterprise financial risk analysis has always been a core research issue in finance. Although there are already some valuable and impressive surveys on risk management, these surveys introduce approaches in a relatively isolated way and lack the recent advances in enterprise financial risk analysis. Due to the rapid expansion of the enterprise financial risk analysis, especially from the computer science and big data perspective, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing enterprise financial risk researches, as well as to summarize and interpret the mechanisms and the strategies of enterprise financial risk analysis in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. This paper provides a systematic literature review of over 300 articles published on enterprise risk analysis modelling over a 50-year period, 1968 to 2022. We first introduce the formal definition of enterprise risk as well as the related concepts. Then, we categorized the representative works in terms of risk type and summarized the three aspects of risk analysis. Finally, we compared the analysis methods used to model the enterprise financial risk. Our goal is to clarify current cutting-edge research and its possible future directions to model enterprise risk, aiming to fully understand the mechanisms of enterprise risk communication and influence and its application on corporate governance, financial institution and government regulation.