Environmentalregulatory agencies have implemented stringent restrictionson the permissible levels of sulfur compounds in fuel to reduce harmfulemissions and improve air quality. Problematically, traditional desulfurizationmethods have shown low effectiveness in the removal of refractorysulfur compounds, e.g., thiophene (TS), dibenzothiophene (DBT), and4-methyldibenzothiophene (MDBT). In this work, molecular dynamics(MD) simulations and free energy perturbation (FEP) have been appliedto investigate the use of ionic liquids (ILs) and deep eutectic solvents(DESs) as efficient TS/DBT/MDBT extractants. For the IL simulations,the selected cation was 1-butyl-3-methylimidazolium [BMIM] and theanions included chloride [Cl], thiocyanate [SCN], tetrafluoroborate[BF4], hexafluorophosphate [PF6], and bis(trifluoromethylsulfonyl)amide[NTf2]. The DESs were composed of choline chloride withethylene glycol (CCEtg) or with glycerol (CCGly). Calculation of excesschemical potentials predicted the ILs to be more promising extractantswith energies lower by 1-3 kcal/mol compared to DESs. IncreasingIL anion size was positively correlated to enhanced solvation of S-compounds,which was influenced by energetically dominant solute-anioninteractions and favorable solute-[BMIM] & pi;-& pi; stacking.For the DESs, the solvent components offered a range of synergistic,yet comparatively weaker, electrostatic interactions that includedhydrogen bonding and cation-& pi; interactions. An in-depthanalysis of the structure of IL and DES systems is presented, alongwith a discussion of the critical factors behind experimental trendsof S-compound extraction efficiency.