This paper reports the differences in combustion characteristics of fossil diesel and the methyl esters of coconut (CME), palm (PME), and soy (SME) over a range of engine conditions. The studies are conducted at a constant engine speed of 2000 rpm, and at engine load values of 0.5 kW (low), 1.5 kW (medium), and 2.5 kW (high). The investigated fuels are CME, PME, and SME at 0% diesel mixture (B100), 50% diesel mixture (B50), and fossil diesel (B0). Here, the OpenFOAM open-source computational fluid dynamics code is utilized to simulate the in-cylinder events. An in-house model for thermophysical and transport properties is employed, along with a mechanism comprising 113 species and 399 reactions with integrated NOx kinetics. Good levels of accuracy are achieved in the prediction of the ignition delay (ID) period, peak pressures, pressure traces, and heat-release rate profiles for all the test fuels. Biodiesel fuels are found to produce larger fuel droplet sizes, longer spray penetration, and lower vaporization rates compared to those of fossil diesel. In terms of the combustion behavior, the ID period decreases as the engine load is increased for neat CME, PME, and SME. However, the ID period increases as the load is raised for the B50 mixtures of CME, PME, and SME. All neat biodiesels and their blends except neat SME produce shorter ID periods than fossil diesel. Changing the fuel type from diesel to biodiesel alter the physical and chemical delay and, hence, the overall ID period. As a result, variations in the combustion behavior between the fuels are recorded.