Summary. Estimating the burden of infectious disease is complicated by the general tendency for underreporting of cases. When the reporting rate is unknown, conventional methods have relied on accounting methods that do not make explicit use of surveillance data or the temporal dynamics of transmission and infection. State space models are a framework for various methods that allow dynamic models to be fitted with partially or imperfectly observed surveillance data. State space models are an appealing approach to burden estimation as they combine expert knowledge in the form of an underlying dynamic model but make explicit use of surveillance data to estimate parameter values, to predict unobserved elements of the model and to provide standard errors for estimates.