Atherosclerosis is one of the principle pathologies of cardiovascular disease with blood cholesterol a significant risk factor. The World Health Organization estimates that approximately 2.5 million deaths occur annually because of the risk from elevated cholesterol, with 39% of adults worldwide at future risk. Atherosclerosis emerges from the combination of many dynamical factors, including haemodynamics, endothelial damage, innate immunity and sterol biochemistry. Despite its significance to public health, the dynamics that drive atherosclerosis remain poorly understood. As a disease that depends on multiple factors operating on different length scales, the natural framework to apply to atherosclerosis is mathematical and computational modelling. A computational model provides an integrated description of the disease and serves as an in silico experimental system from which we can learn about the disease and develop therapeutic hypotheses. Although the work completed in this area to date has been limited, there are clear signs that interest is growing and that a nascent field is establishing itself. This article discusses the current state of modelling in this area, bringing together many recent results for the first time. We review the work that has been done, discuss its scope and highlight the gaps in our understanding that could yield future opportunities.