<p>Research on copulas and their applications, particularly in competing risks modeling, remains an active area of investigation across probability, statistics, and stochastic processes. This review synthesises the literature on copula-based competing risks models, focusing on <i>identifiability</i>, estimation, and applications. We systematically examine how copulas provide a flexible framework for modeling dependence structures among latent failure times. This will enable researchers to address the <i>identifiability</i> crisis through various strategies, including a known copula. We provide an extensive survey of applications across survival analysis, reliability engineering, and other fields, supported by an interactive table of references. A simulation study demonstrates that the Copula Graphic estimator performs well when the copula family and dependence parameter are correctly specified. Furthermore, it highlights the severe bias of traditional methods under dependent censoring. A real-data application illustrates practical implementation. Finally, key research directions are provided.</p>