This chapter provides an in-depth review of the epidemiological models utilized for predicting and managing epidemic infectious diseases, with a particular emphasis on Susceptible-Infected-Recovered (SIR) models and their various facets. The objectives of this review are threefold: (1) the assumptions, equations, and methodologies for estimating critical parameters within these models are evaluated; (2) the challenges associated with implementing disease control interventions, including both medical and non-medical strategies, and their integration into the models are explored; and (3) relation of SIR models and optimization models are investigated. Additionally, a systematic review at the micro-level has identified significant research gaps within the existing literature, leading to recommendations for future research directions. One of the most important findings is that many assumptions need to be reviewed to be better aligned with real conditions, which should hopefully stimulate some useful inquiries into how to model epidemic diseases.