When facing the global health threat posed by an infectious disease, predictive mathematical models are crucial not only to understand and forecast the epidemic evolution, but also to plan effective control strategies that contrast the disease and its spread in the population. This tutorial aims to give a broad overview of the fundamental developments enabled by systems-and-control methodologies in modelling and controlling epidemiological dynamics across scales, from infection dynamics within hosts to contagion dynamics between hosts. The first part is focused on modelling and control of infectious diseases in the host, capturing the dynamic interplay between pathogens and the immune system, and discussing control strategies to design tailored therapies and treatments to optimally clear the infection. The second part deals with the spread of contagion between hosts: epidemic dynamics are modelled resorting to networked systems where the nodes represent individuals and the links represent interactions that can lead to contagion, and a comparison to compartmental models is carried out. The third part surveys multi-scale models and multi-pronged approaches to contrast the spread of infectious diseases: a holistic perspective is adopted, including behavioural and socioeconomic aspects along with public health issues, to discuss optimal epidemic control across scales.