The main characteristics of ebullated bed reactors have been reviewed in this work. Key factors of the application of these reactors to hydrocracking of heavy petroleum fractions, such as sediments formation, catalyst attrition and catalyst deactivation, have been clearly discussed. Mathematical representation of ebullated bed systems has been organized into hydrodynamics, scaling down and reactor modeling. Only a few reports dealing with the topic of this review were found in the literature, which employ different levels of sophistication to establish the model equations. These literature reports were summarized and properly discussed, from which it has been recognized that modeling of ebullated bed reactors is a complex task and deserves more attention.