The COVID-19 pandemic demonstrated the key role that epidemiology and modelling play in analysing infectious threats and supporting decision making in real-time. Motivated by the unprecedented volume and breadth of data generated during the pandemic, we review new analytic opportunities and methodologicaldevelopments available to address questions that emerge during a major modern epidemic. Following the broad chronology of insights required - from understanding initial dynamics to retrospective evaluation of interventions, we describe the theoretical foundations of each approach and the underlying intuition. Througha series of case studies, we illustrate real life applications, and discuss implications for future work.