The equilibrium structure and interconversion tunneling of the van der Waals dimer of sulphur dioxide is investigated. Results with the electrostatic model are compared with those obtained ab initio at the self-consistent field level and with second order Moller-Plesset perturbation theory. This complex is shown to be a difficult problem for theoretical chemistry. We have located six stationary points on the dimer surface, two of which are probably transition states. The lowest energy region is very flat at all levels of theory but dispersion forces are likely to be responsible for the observed C(s) symmetry global minimum. Substantial vibrational averaging must be invoked to explain the observed dipole moment. The tunneling splittings can be explained by a single motion proceeding via a centrosymmetric transition state and analogous to the internal rotation of acetylene dimer. A model potential gives a value of 56 cm-1 for the barrier, within the range predicted ab initio. We have also investigated three cyclic structures of the SO2 trimer, two of which are minima. The global minimum is probably nonsymmetric.