Rocket engines and high-power new generations of jet engines and diesel engines oftentimes involve the injection of one or more reactants at subcritical temperatures into combustor environments at high pressures, and more particularly at pressures higher than those corresponding to the critical points of the separate components, which typically range from 13 to 50 bars for most propellants. This class of trajectories in the thermodynamic space has been traditionally referred to as transcritical. However, the fundamental understanding of fuel atomization, vaporization, mixing, and combustion processes at such high pressures remains elusive. A theory of the transcritical hydrodynamics of propellants in high-pressure combustors will be presented in this talk. This theory couples the multicomponent Navier-Stokes conservation equations with an extended version of the diffuse-interface theory of van der Waals. Technological factors that motivate the investigation of this problem will be outlined, and fundamental transcritical flow structures revealed by this theory will be discussed.