In this talk I will present some of my recent work with various research groups on hepatitis B virus (HBV), and discuss how different components of the body’s immune system try to clear this infection. Currently approximately 400 million people are infected with HBV. Antiviral therapies against HBV are mostly unsuccessful, so a better understanding of the processes the immune system employs in its fight against this disease can only be to our advantage. Another aspect of my talk will be to comment on how my experience in this "real world problem" correlates with what we teach our students in Applied Mathematics. In particular I will discuss how the areas of Dynamical Systems, Optimization and Statistics are relevant to investigations of infectious diseases.