As COVID-19 rapidly spread all around the world, different methods have been proposed to explore the dynamics of the pandemic, understand the transmission mechanism, and assess the preventive measures. Mathematical models are frequently used worldwide to predict various parameters and develop effective policies for disease control. Compartmental models are the most popular mathematical models in epidemiology. These models divide the population into distinct groups (compartments) based on their status and describe the movement of an individual from one compartment to another. Various compartmental models and their variations have been developed to model the pandemic dynamics and measure the efficiency and necessity of different initiatives such as lockdowns, face masks, and vaccination. This paper provides a systematic literature review on different compartmental models proposed to model the COVID-19 pandemic. These models are discussed in detail based on the compartmental structure in the model, aim of the model, variables, and methodological approaches.