In this paper we propose, to the best of our knowledge, the first analysis of the global networks of integrators FedEx, UPS, and DHL using network science. While noticing that all three networks rely on a “hub-and-spoke” structure, the network configuration of DHL leans towards a multi-“hub-and-spoke” structure that reflects the different business strategy of the integrator. We also analyzed the robustness of the networks, identified the most critical airports per integrator, and assessed that the network of DHL is the most robust according to our definition of robustness. Finally, given the unprecedented historical time that the airline industry is facing at the moment of writing, we provided some insights into how the COVID-19 pandemic affected the global capacity of integrators and other cargo airlines. Our results suggest that full-cargo airlines and, much more dramatically, combination airlines were impacted by the pandemic. On the other hand, apart from fluctuations in offered capacity due to travel bans that were quickly recovered thanks to the resilience of their networks, integrators seem to have escaped the early months of the pandemic unscathed.