Whenever you are infected by a viral pathogen, your adaptive immune system initiates an evolutionary process that reliably produces antibodies that are effective at neutralizing that pathogen. This protects you against future infections by similar strains. However, as the virus spreads through a population, these responses create population-wide immunity which leads to a selective pressure on the virus to evolve in ways that evade this immune protection. This viral evolution in turn drives further shifts in our immune responses. This continuous process of viral-immune coevolution drives the dynamics of diseases such as Influenza and SARS-CoV-2. I will describe how systematic measurements of high-dimensional protein sequence-function landscapes relevant for the molecular interactions between human antibodies and viral antigens can help us understand this coevolutionary process. We will focus in particular on the evolution of broadly neutralizing anti-influenza antibodies, and on the evolutionary dynamics that led to the emergence of the Omicron variant of SARS-CoV-2.