The theory of the vibration-rotation states of atom-spherical top van der Waals complexes is developed. The exact close-coupled equations are closely analogous to those encountered in atom+spherical top scattering. The structure of the coupled equations is investigated, and close-coupling calculations of the bound states of Ar-CH4 are presented for two different intermolecular potentials. The role of symmetry in the complex is discussed, and the energy levels are interpreted using a model in which the CH4 molecule undergoes hindered rotation in the field of the Ar atom. Correlation diagrams are presented, showing how the free-rotor levels are converted into near-rigid vibrational energy levels as the anisotropy of the intermolecular potential increases. The effect of higher-order anisotropic terms is investigated, and correlation diagrams are given for complexes of tetrahedral, octahedral, and icosahedral molecules. The role of monomer vibrational angular momentum is investigated.