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This paper reviews the basic physical notions underlying microwave sintering and the theoretical and numerical models of the microwave sintering process. The propagation and absorption of electromagnetic waves in materials, and the distribution of electromagnetic field in cavity resonators that serve as applicators for microwave processing are discussed and the electromagnetic modeling of such applicators is reviewed. The microwave absorption properties of ceramic and metal powder materials and the methods of their description are addressed. Self-consistent electromagnetic and thermal models that are capable of predicting the temperature distribution in the microwave-heated materials and dynamic effects such as thermal runaway instabilities are reviewed. The multiphysics simulations that combine electromagnetic, thermal, and sintering models and result in predicting densification, shrinkage, and grain structure evolution are discussed in detail. The significance of microwave nonthermal effects in sintering is demonstrated based on the experimental results, and the models of such effects are reviewed. [ABSTRACT FROM AUTHOR]