Continuum-solvent models (CSMs) have successfully predicted many quantities, including the solvation-free energies (ΔG) of small molecules, but they have not consistently succeeded at reproducing experimental binding free energies (ΔΔG), especially for protein-protein complexes. Several CSMs break ΔG into the free energy (ΔGvdw) of inserting an uncharged molecule into solution and the free energy (ΔGel) gained from charging. Some further divide ΔGvdw into the free energy (ΔGrep) of inserting a nearly hard cavity into solution and the free energy (ΔGatt) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein-protein complexes neither ΔGrep nor ΔGvdw was linear in the solvent-accessible area A, as assumed in many CSMs, and the corresponding components of ΔΔG were not linear in changes in A. We show that linear response theory (LRT) yielded good estimates of ΔGatt and ΔΔGatt, but estimates of ΔΔGatt obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of ΔGel differed by more than 100 kcal/mol from the explicit solvent model's (ESM's) predictions, and its estimates of the corresponding component (ΔΔGel) of ΔΔG differed by more than 10 kcal/mol. Finally, the Poisson-Boltzmann equation produced estimates of ΔGel that were correlated with those from the ESM, but its estimates of ΔΔGel were much less so. These findings may help explain why many CSMs have not been consistently successful at predicting ΔΔG for many complexes, including protein-protein complexes.