How are economies in a modern age impacted by epidemics? In what ways is economic life disrupted? How can pandemics be modeled? What can be done to mitigate and manage the danger? Does the threat of pandemics increase or decrease in the modern world? The Covid-19 pandemic has demonstrated the importance of these questions and the potential of complex systems science to provide answers. This article offers a broad overview of the history of pandemics, of established facts, and of models of infection diffusion, mitigation strategies, and economic impact. The example of the Covid-19 pandemic is used to illustrate the theoretical aspects, but the article also includes considerations concerning other historic epidemics and the danger of more infectious and less controllable outbreaks in the future.