Solid-state anaerobic digestion (SS-AD) technology for the conversion of solid organic wastes to renewable energy has been widely studied and applied during the past decades. Due to the nature of the solid medium, the SS-AD process is significantly different from the traditional liquid anaerobic digestion in many aspects, such as the distribution of microbes and substrates in the reactors, mass transfer, and reaction kinetics. Extensive efforts have been dedicated to developing mathematical models for understanding SS-AD mechanisms, predicting its performance, and improving process control. In this review, SS-AD mathematical models derived from theoretical, empirical, and statistical approaches are critically reviewed and discussed regarding their different assumptions, structures, applications, and limitations. Based on this review, it was concluded that significant efforts should be devoted to experimental verification of the model assumptions, measurement of important kinetic parameters specific for SS-AD, and generation of sufficient data for model validation. It is necessary to synergistically improve modeling and experimental approaches in order to gain deeper insight into the SS-AD mechanism. Several promising research directions for the future development of experimental and modeling approaches in SS-AD are proposed. (C) 2015 Elsevier Ltd. All rights reserved.