In the era of big data, survival analysis, a statistical method for analyzing the expected duration of time until one or more events happen, has gained significant importance, especially in medical and biological research. This paper primarily focuses on the comprehensive exploration and understanding of survival analysis modelling, from traditional to modern approaches, and identifies the existing challenges and future prospects of these models. We commence by discussing foundational models such as the Kaplan-Meier and Cox proportional hazards models, and then transition into the exploration of the more flexible Accelerated Failure Time model. Acknowledging the current challenges faced in survival analysis, such as dealing with high-dimensional data, lack of labelled data, and data quality and reliability, we further delve into the potential solutions provided by modern techniques like deep learning, transfer learning, and semi-supervised learning. Additionally, the paper highlights the issues of interpretability and transparency of complex models, offering an overview of interpretability methods such as LIME and SHAP. Despite certain limitations, our study offers a valuable reference for understanding the evolution of survival analysis and sparks further discussions about its future development, emphasizing the profound significance of survival analysis in the realm of statistical research.