In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL), as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly-interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogenous set of reference interaction energies were computed for the supramolecular complexes constituting the L7 and SL12 data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (especially for the S12L set) have been determining for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 This is a previous version of the article published in Journal of Chemical Theory and Computation. 2015, 11(3): 932-939. doi:10.1021/acs.jctc.5b00002 2 evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy.Overall, the nonlocal van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly-bonded supramolecular systems.