Mathematical models have many applications in infectious diseases: epidemiologists use them to forecast outbreaks and design containment strategies; systems biologists use them to study complex processes sustaining pathogens, from the metabolic networks empowering microbial cells to ecological networks in the microbiome that protects its host. Here, we (1) review important models relevant to infectious diseases, (2) draw parallels among models ranging widely in scale. We end by discussing a minimal set of information for a model to promote its use by others and to enable predictions that help us better fight pathogens and the diseases they cause.