Among oxygenated fuels, the simplest ether fuel, dimethyl ether (DME), is often regarded as the next generation fuel because of its superior soot emission characteristics. However, DME has distinctly different spray combustion characteristics from the conventional hydrocarbon liquid diesel fuels in terms of evaporation, ignition, high vapor pressure, cetane number, oxygenate ingredient, heat release rate, liquid density, etc. In the present study, to understand the overall spray combustion characteristics of DME fuel as well as to identify the distinctive differences of DME combustion processes compared to conventional hydrocarbon liquid fuels, the sequence of the comparative analysis has been systematically made for DME and n-heptane liquid fuels. To realistically represent the physical processes involved in the spray combustion, this study employs the hybrid breakup model, the stochastic droplet tracking model, collision model, high-pressure evaporation model, and transient flamelet model with detailed chemistry. On the basis of numerical results, the detailed discussions are made in terms of the evaporation characteristics of a single droplet at high-pressure, combustion processes, ignition characteristics of homogeneous mixtures and spray jets, flame structure, and turbulence-chemistry interaction in the n-heptane and DME-fueled spray combustion processes.