Heterogeneity plays a vital role in the epidemiology of infectious diseases. Individual- level variation in susceptibility or infectiousness due to predictable biological, behavioural or random factors can modify the transmission dynamics and cause deviation from what is expected from models assuming that transmission is homogeneous. One of the important sources of heterogeneity are social contact networks; respiratory infectious diseases including influenza and COVID-19 spread over social contact networks that are formed through mixing in multiple social settings. Households and schools are important places of transmission of many respiratory infectious diseases (although the role of schools in the transmission of COVID-19 remain unclear). Schoolchildren are often the main drivers of influenza epidemics, and they further spread the disease to other age groups by introducing infection into households and other settings. However, detailed transmission dynamics in households and schools have not been fully understood; in particular, it is not well known how group sizes and contact patterns affect transmission risks in heterogeneous populations. The underlying mechanisms of variations in transmission may not necessarily be explained by known factors. Even in such cases, quantifying such variation can be useful in characterising the transmission dynamics. SARS-CoV-2, along with other related coronaviruses, exhibits strong dispersion in the number of secondary transmissions per case. In addition to the basic reproduction number R0, which represents the mean number of secondary transmissions in fully susceptible population, the degree of variability around the mean highlights the importance of superspreading and potentially informs control policy targeting superspreading events. This PhD study attempts to further improve the current understanding of how heterogeneity affects transmission dynamics, inference and public health applications. Using datasets and models of high burden respiratory infectious diseases, influenza and COVID-19, this thesis investigated the roles of heterogeneity in various contexts, i.e. transmission settings such as households and schools and important research topics such as vaccine evaluation studies, international dissemination and contract tracing.