Neutrophils are antimicrobial immune cells, as demonstrated by more than 100 years of research. We are witnessing now a revolution in how immune cells and organismal physiology interact with each other, even when no infection or injury occurs. In this virtual seminar we will discuss this important novel concept in Immunology and present the recent work carried out at the (Centro Nacional de Investigaciones Cardiovasculares Carlos III (CNIC)) demonstrating that neutrophils, the most abundant type of leukocytes, perform many more functions besides fighting infections. State of the art transcriptome and proteome analyses at the single cell level, as well as studies of the cells' chromatin, show that neutrophils acquire unique properties in each tissue, and that this is relevant for many biological processes, such as vessel formation or the production of blood. We also apply statistical analyses and simple mathematical models to estimate what these changes at the single cell level imply in terms of phenotype, biological diversity and cellular lifespan across different organs. With these tools we attempt to provide a more accurate view of what immune cells really do, and how. Applied Mathematicians working at the interface of Biomathematics and Immunology will find a number of open problems waiting to be tackled with more sophisticated modelling approaches.