This contributed volume investigates several mathematical techniques for the modeling and simulation of viral pandemics, with a special focus on COVID-19.  Modeling a pandemic requires an interdisciplinary approach with other fields such as epidemiology, virology, immunology, and biology in general.  Spatial dynamics and interactions are also important features to be considered, and a multiscale framework is needed at the level of individuals and the level of virus particles and the immune system.  Chapters in this volume address these items, as well as offer perspectives for the future.