Infectious disease-causing pathogens have plagued humanity since antiquity, and the COVID-19 pandemic has been a vivid reminder of this perpetual existential threat. Vaccination has saved more lives than any other medical procedure, and effective vaccines have helped control the COVID-19 pandemic. However, we do not have effective vaccines against rapidly mutating viruses, such as HIV; nor do we have a universal vaccine against seasonal variants of influenza or SARS-CoV-2 variants that may evolve in the future. The ability to develop effective vaccines that protect us from highly mutable viruses will help create a more pandemic-resilient world. I will describe how by bringing together approaches from statistical physics, virology and immunology, progress is being made to address this challenge. I will focus on broadly protective antibody responses. First, I will describe some general principles and then I will discuss how by combining physics-based modeling and data from humans who received COVID vaccines we are learning new mechanisms underlying the antibody response upon infection or vaccination.