Mathematical modelling has played a pivotal role in understanding the epidemiology of and guiding public health responses to the ongoing coronavirus disease of 2019 (COVID-19) pandemic. Here, we review the role of epidemiological models in understanding evolving epidemic characteristics, including the effects of vaccination and Variants of Concern (VoC). We highlight ways in which models continue to provide important insights, including 1) calculating the herd immunity threshold and evaluating its limitations; 2) verifying that nascent vaccines can prevent severe disease, infection, and transmission but may be less efficacious against VoC; 3) determining optimal vaccine allocation strategies under efficacy and supply constraints; and 4) determining that VoC are more transmissible and lethal than previously circulating strains, and that immune escape may jeopardize vaccine-induced herd immunity. Finally, we explore how models can help us anticipate and prepare for future stages of COVID-19 epidemiology (and that of other diseases) through forecasts and scenario projections, given current uncertainties and data limitations.