Underground coal gasification can convert deep coal into synthesis gas for use in the production of electricity, fuels and chemicals. This paper provides a review of the fundamental physical phenomena in underground coal gasification and associated modeling efforts. The relevant fundamentals of coal gasification are described and the phenomena of cavity growth at the sidewall and roof of the underground cavity are examined in detail. The transport phenomena and chemical reactions occurring in the permeable bed of char and ash and the void space are reviewed. The modeling of the transport of heat and mass, including contaminants, in the near- and far-fields surrounding an underground coal gasifier are also summarized. An overview of the geomechanical phenomena and the coupled interactions between transport and mechanical phenomena are provided. Finally, integrated UCG models are reviewed and recommendations for future model development are provided.