Experimental data on micellization in aqueous solutions of 1-alkyl-3-methylimidazolium salts [C_nmim]X and their mixtures with sodium dodecyl sulfate (NaDS) are reviewed. New results (the critical micelle concentration and enthalpy of micellization) are presented for mixtures of [C₄mim]PF₆, [C₆mim]BF₄, [C₆mim]Br and [C₁₀mim]Br with NaDS. Our data cover a wide range (from 0 to 0.9) of solvent-free based mole fractions of ionic liquid (IL). Even very small addition of ILs substantially decreases the cmc of NaDS due to the combined effect of electrostatic and hydrophobic interactions, and formation of mixed micelles. It is shown that the quasichemical aggregation model by Nagarajan and Ruckenstein may be successfully applied to aqueous solutions of long-chain ILs and their mixtures with NaDS. The local structure of micelles is obtained from all-atom MD simulations for [C_nmim]Br and [C_nmim]X + NaDS in aqueous medium.