This paper addresses the physiochemical mechanisms involved in transcritical and supercritical vaporization, mixing, and combustion processes in contemporary liquid-fueled propulsion and power-generation systems. Fundamental investigation into these phenomena poses an array of challenges due to the obstacles in conducting experimental measurements and numerical simulations at scales sufficient to resolve the underlying processes. In addition to all of the classical problems for multiphase chemically reacting flows, a unique set of problems arises from the introduction of thermodynamic nonidealities and transport anomalies. The situation becomes even more complex with increasing pressure because of an inherent increase in the flow Reynolds number and difficulties that arise when fluid states approach the critical mixing condition. The paper attempts to provide an overview of recent advances in theoretical modeling and numerical simulation of this subject. A variety of liquid propellants, including hydrocarbon and cryogenic fluids, under both steady and oscillatory conditions, are treated systematically. Emphasis is placed on the development of a hierarchical approach and its associated difficulties. Results from representative studies are presented to lend insight into the intricate nature of the problem.