In the present study, we report tests of 57 model chemistry methods for calculating binding energies of 31 diverse van der Waals molecules arranged in five databases of noncovalent interaction energies. The model chemistries studied include wave function theory (WFT), density functional theory (DFT), and combined wave function-density-functional-theory (CWFDFT), and they include methods whose computational effort scales (for large systems) as N7, N6, N5, and N4, where N is the number of atoms. The model chemistries include 2 CWFDFT N7 models, 4 multilevel WFT N7 models, 5 single-level WFT N7 models, 4 CWFDFT N 6 models, 3 multilevel WFT N6 models, 11 single-level WFT N6 models, 5 CWFDFT N5 models, 10 single-level WFTN 5 models, 4 multilevel WFT N5 models, 4 single-level DFT N4 models, and 5 single-level WFT N4 models. We draw the following conclusions based on the mean absolute errors in 31 noncovalent binding energies: (1) MCG3-MPW gives the best performance for predicting the binding energies of these noncovalent complexes. (2) MCQCISD-MPWB and MCQCISD-MPW are the best two N6 methods. (3) M05-2X is the best single-level method for these noncovalent complexes. These four methods should facilitate useful calculations on a wide variety of practical applications involving hydrogen bonding, charge-transfer complexes, dipole interactions, weak (dispersion-like) interactions, and π⋯π stacking. If a user is interested in only a particular type of noncovalent interactions, though, some other methods, may be recommended for especially favorable performance/cost ratios. For example, BMC-CCSD has an outstanding performance for hydrogen bonding, and PWB6K has an outstanding cost-adjusted performance for dipole interaction calculations on very large systems. We also show that M05-2X performs well for interactions of amino acid pair residues.