The present paper reviews recent achievements in numerical modeling of super- and transcritical injection processes during the last 20 years. First, it provides an overview of various methods and modeling for describing the turbulent flow evolution of supercritical fluid injection essentially issuing from supercritical pressure environments. Since highly unsteady and complex flow and mixing as well as combustion processes are in play, this paper restricts itself to scale-resolved modeling based on large eddy simulation (LES) technique. Primarily, the extended thermodynamics framework is introduced to evaluate the consistency of existing LES models usually used in computational fluid dynamics to also simulate turbulent supercritical fluid flows. Under consideration of issues associated with the nonidealities in thermodynamic and transport properties, the numerical challenges are discussed. In particular, some numerical issues are highlighted to assess the effect of different numerical schemes and spatial resolutions on the mixing process prediction. Overall, this part shows that LES has proved to deliver in a satisfactory way the flow/mixing properties and some combustion features. To describe the liquid fuel jet's evolvement, different existing modeling routes are categorized in terms of mixing description, two-phase appearance, and possible phase coupling. It turns out that both the ratio of the thermal-entrance to liquid-core lengths and the competition between the characteristic time of jet breakup and that of the interfacial tension degradation are key parameters that may determine how the supercritical thermodynamic conditions can be reached by a spray jet while revealing the significance of transcritical dynamics. Second, this paper exploits the second law of thermodynamics via the entropy inequality in order to show how an entropy generation analysis can be used to reveal the effect chain of processes evolving, to identify the causes of irreversibilities, and to determine process regimes beneficial for mixing and/or other selected processes. This is demonstrated to be exemplary in the case of a single component supercritical injection process from which a physical model is derived. Useful inferences and some challenges are highlighted.