Many viruses exhibit substantial antigenic variation, resulting in phenotypic differences between related variants of the same species. This variability poses a substantial public health burden, as hosts can be reinfected many times over their lifetime. In this thesis, I use mathematical models to capture unobserved biological processes in two antigenically variable systems: Zika and influenza. In Chapter 3, I develop a model linking Zika virus infection and the gestational risk of microcephaly. Through fitting this model to incidence data from South America, I find inconsistencies in the gestational risk profiles inferred for different locations. Motivated by the question of how prior exposure influences subsequent disease, I turn to the problem of understanding influenza exposure histories. In Chapter 4, I fit antibody kinetics models to serological data from ferrets exposed to multiple infections and vaccinations. I generate estimates for immunological parameters that may be important in explaining human antibody dynamics arising from repeated unobserved exposures. Validating these models motivates their application in human populations. Chapter 5 develops a robust statistical framework to identify unobserved influenza infections using routinely collected serological data. Model assumptions for infection histories are an important consideration, and I thoroughly explore the underlying behaviour of the inference method. Finally, in Chapter 6, I use this model to infer influenza infection histories for 1,130 individuals in southern China. This enables the reconstruction of historical influenza A/H3N2 incidence, revealing epidemiological patterns that vary across individual ages and at a small spatial scale. Together, these results demonstrate how integrating modern statistical methods, immunology and seroepidemiology may help to answer public health questions. Improved analytical methods for serological data, such as those developed in this thesis, may provide a rich new stream of augmented data and generate new insights into the life course epidemiology of antigenically variable pathogens.