The choice of a modeling approach is driven by the oil policy or market question that needs to be addressed. We provide the non-modeling community with insightful information on oil market models, shedding light on the economic interpretation of technical aspects (such as the meaning of the costs associated with certain types of constraints), but without introducing any mathematical formulations. We also emphasize the reasonings and assumptions underlying the modeling structures and solutions proposed in the literature. We first review how models have usually represented market fundamentals. We then examine recent modeling developments addressing market issues (such as the impact of the shale oil revolution and the shift in producers’ behavior) and policy questions (such as the use of spare capacity to stabilize prices, the lifting of export controls, and the management of uncertainties surrounding the energy transition) that have emerged since the Great Recession.