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Removing sulfur compounds from petroleum is essential in mitigating harmful emissions linked to fuel combustion. Problematically, thiophenic compounds that are readily present in fossil fuels resist conventional desulfurization methods. Extractive Desulfurization (EDS) provides an attractive alternative that can be selective for heterocyclic sulfur compounds, i.e., thiophene and its derivatives, through the choice of solvent employed. To this end, a burgeoning field has developed around the use of ionic liquids (ILs) given their ability to be fine-tuned with varying levels of polarity and solubility to suit the specific requirements of the desulfurization process. Hundreds of experimental studies featuring the use of IL technologies have provided encouraging trends for the design of more efficient extractants; however, conflicting data and a lack of a definitive understanding of important solute-ion interactions has presented challenges in advancing the field. More recently, computational investigations have been employed to unravel these key interactions and to inform design principles for future high-performance IL extractants. The myriad of intermolecular forces, e.g., coulombic, dispersive, and steric, and their subtle interplay present in IL-mediated EDS processes are prime for study using computational methodologies that include quantum mechanics (QM) at the ion-solute interaction level, molecular dynamics (MD) for the simulation of bulk-phase solvent properties, and the Conductor-Like Screening Model (COSMO) for high-throughput screening. This minireview summarizes computational advances and findings in the field of IL-mediated EDS in a format suitable for theoreticians and experimental chemists alike with discussions provided of future directions for the field.