Partition coefficients, as values of log P, between water and two room-temperature ionic liquids and between water and an aqueous biphasic system have been correlated with Abraham's solute descriptors to yield linear free energy relationships that can be used to predict further values of log P, to ascertain the solute properties that lead to increased or decreased log P values, and to characterize the partition systems. It is shown that, in all three of the systems, an increase in solute hydrogen-bond basicity leads to a decrease in log P and an increase in solute volume leads to an increase in log P. For the two ionic liquid systems, an increase in solute hydrogen-bond acidity similarly decreases log P, but for the aqueous biphasic system, solute hydrogen-bond acidity has no effect on log P. These effects are rather smaller than those observed in traditional water-solvent systems. However, the ionic liquids appear to have an increased affinity for polyaromatic hydrocarbons as compared to traditional organic solvents. Principal component analysis and nonlinear mapping show that the three unconventional partition systems are considerably different from conventional water-organic solvent systems.