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 modern opportunities for analysis 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. Through a series of case studies, we illustrate real life applications, and discuss implications for future work.