A wide range of infectious diseases are monitored at the local, state, and national levels using disease surveillance systems designed to asses current disease burden and to detect emerging outbreaks. Public health officials rely on surveillance data to provide accurate and timely information, which may then be used to inform policy or intervention decisions. For privacy reasons, surveillance data is often aggregated over space and time; hence the data is limited to basic demographic information along with basic spatial or temporal information, such as the county of residence for an infected individual and week of diagnosis. The limited information contained within, and potential bias of, surveillance data can pose serious challenges to valid inference. Nevertheless, for many practical applications, surveillance networks are one of the best sources of data, especially at the state or local level. In this dissertation, we develop models to obtain timely estimates of parameters of interest using infectious disease surveillance data. This work is motivated by surveillance data for hand, foot, and mouth disease (HFMD) in China, influenza in Florida, and measles in Germany. For HFMD, we develop a model to quickly estimate pathogen-specific disease counts, and associations with meteorological variables, when laboratory information is available for only a small subsample of cases. For the flu, we consider approaches to account for potential biases in the data due to disparities in healthcare access. For measles, we develop an ecological model to account for differing levels of vaccination coverage while providing estimates of key epidemic parameters.