This paper provides an overview of recent advances in the theoretical modeling and numerical simulation of cryogenic fluid injection and mixing in transcritical and supercritical environments. The basis of the analysis is a general theoretical and numerical framework that accommodates full conservation laws and real-fluid thermodynamic and transport phenomena. All of the thermophysical properties are determined directly from fundamental thermodynamics theories, along with the use of corresponding-state principles. Turbulence closure is achieved using a large-eddy-simulation technique, in which large-scale motions are calculated explicitly and the effects of unresolved small-scale turbulence are modeled either analytically or empirically. The analysis has been applied to study: (1) fluid jet dynamics, (2) swirl injection of liquid oxygen through a simplex swirl injector, and (3) shear co-axial injection and mixing of liquid oxygen and methane. Various effects, including density stratification, shear-layer instability, volume dilatation, and property variations, dictating the evolution of cryogenic jets and mixing layers, are identified and analyzed in depth. The jet dynamics are found to be largely determined by the local thermodynamic state through its influence on the thermophysical properties of the fluid. The impact of injector configuration and operating conditions on the swirl injector behavior are also highlighted. These results not only shed light on the subject problems, but also provide a quantitative basis for identifying the design parameters and flow variables that exert the strongest influence on the underlying processes.