I will review how outbreak modelling has evolved over the last two decades, and discuss the drivers leading to the more complex computational simulations being increasingly used in preferences to simpler compartmental models of disease transmission. The demand for increased model 'realism' and therefore complexity poses challenges for model parameterisation and validation, so I will give an overview of the data needs for current models and how application of modern inferential methods is giving greater insight into the details of transmission processes than ever before. I will discuss how data limitations, intrinsic stochasticity plus uncertainties about disease biology, mechanisms of transmission and the impact of controls limit our ability to predict detailed patterns of epidemic spread. Throughout my lecture, I will draw on the examples of work undertaken on pandemic influenza and other emerging infectious disease outbreaks over the last few years.