The increasing complexity of infectious disease transmission calls for advanced modeling frameworks that move beyond static assumptions. Temporal Dynamic Networks (TDNs) have emerged as a useful tool for capturing the dynamics of contact structures that drive epidemic spread. This survey critically examines the state-of-the-art applications of TDNs in modeling infectious diseases, focusing on computational advances such as machine learning, agent-based models, graph neural networks, and hybrid models. We shed light on the theoretical insights that can enhance the understanding and application of these frameworks. This study discusses real-world applications of these models in epidemiology and contends that more concerted effort is required by stakeholders to combat and mitigate the risk of disease resurgence.