The spread of an infection within an organism represents a complex dynamical system comprising various factors across multiple scales: Pathogens have to find appropriate target cells to multiply, immune responses get activated and try to clear the invading pathogen, but thereby need to be tightly regulated in order not to cause substantial damage to the organism. Analyzing experimental and clinical data with mathematical methods and computational models has been essential to get a systematic and quantitative understanding of the biological processes involved during specific infections, and to identify key processes determining disease progression and therapeutic targets. In my talk, I will present mathematical methods that we have developed and used to study different aspects of infection and immune dynamics. In particular, I will focus on the development of spatially explicit multiscale models that allow us to analyze the spread of a virus within a specific tissue environment, such as the spread of the hepatitis C virus within the human liver. Combining experimental and clinical data from various sources by methods from spatial statistics, population dynamic models and computational simulations, we aim at inferring in vivo infection dynamics from static tissue biopsy samples. I will outline the results that have already been obtained, and the experimental and mathematical challenges that still need to be solved.