Internal combustion engines, due to their high energy density, will remain the primary propulsion technology in the near future. To reduce their environmental impact, emerging technologies, such as direct-injected (DI) compressed natural gas (CNG) engines and so-called bio-hybrid fuels from renewable electricity and bio-based carbon sources, offer potentially high thermal efficiency and low pollutant emissions. Gaseous fuel injection with supersonic flows has a strong influence on in-cylinder turbulence, mixing, and combustion. Numerical simulations can help to characterize the high-speed gas jets and use them advantageously in the design of DI-CNG engines. However, such simulations are numerically challenging and compute-intensive due to the presence of shocks as well as small time and length scales. On the other hand, the design of low-carbon liquid fuels for a combustion process requires rapid and repeated evaluation of new candidates over a wide range of conditions, which is not always possible due to several reasons, e.g., limited availability of fuels, adaptation required in combustion systems, or compute-intensive three-dimensional (3D) simulations. This dissertation focuses on the development of reduced-order models (ROMs) that enable faster simulations of DI-CNG engines and rapid screening of the novel fuel candidates for compression ignition engines. The first part of the dissertation is devoted to the fundamental understanding of gas injection using resolved simulations and the subsequent development of ROMs for the fuel injection in engine simulations. The second part presents a cross- sectionally averaged reactive turbulent spray (CARTS) model for transient inert and reactive sprays in compression ignition engines.