Since the start of the still ongoing COVID-19 pandemic, there have been many modeling efforts to assess several issues of importance to public health . In this work, we review the theory behind some important mathematical models that have been used to answer questions raised by the development of the pandemic . We start revisiting the basic properties of simple Kermack-McKendrick type models . Then, we discuss extensions of such models and important epidemiological quantities applied to investigate the role of heterogeneity in disease transmission e.g . mixing functions and superspreading events, the impact of non-pharmaceutical interventions in the control of the pandemic, vaccine deployment, herd-immunity, viral evolution and the possibility of vaccine escape . From the perspective of mathematical epidemiology, we highlight the important properties, findings, and, of course, deficiencies, that all these models have.