What happens at the ionic-liquid (IL)/water interface when the Eu3+ cation is complexed and extracted by bis(dimethyltriazinyl) pyridine "BTP" ligands has been investigated by molecular dynamics and potential of mean force simulations on the interface crossing by key species: neutral BTP, its protonated BTPH+ form, Eu3+, and the Eu(BTP)33+ complex. At both the [BMI][Tf2N]/water and [OMI][Tf2N]/water interfaces, neither BTP nor Eu(BTP)33+ are found to adsorb. The distribution of Eu(BTP)23+ and Eu(BTP)3+ precursors of Eu(BTP)33+, and of their nitrate adducts, implies the occurrence of a stepwise complexation process in the interfacial domain, however. The analysis of the ionic content of the bulk phases and of their interface before and after extraction highlights the role of charge buffering by interfacial IL cations and anions, by different amounts depending on the IL. Comparison of ILs with octanol as the oil phase reveals striking differences regarding the extraction efficiency, the affinity of Eu(BTP)33+ for the interface, the effects of added nitric acid and of counterions (NO3- vs Tf2N-), charge neutralization mechanisms, and the extent of "oil" heterogeneity. Extraction into octanol is suggested to proceed via adsorption at the surface of water pools, nanoemulsions, or droplets, with marked counterion effects.