Abstract Lattice gas models are constructed for multilayer physisorption and solved using Migdal-Kadanoff renormalization group transformations. The Ising lattice gas and solid-on-solid models as well as a more realistic case modeling Kr on graphite are treated. Wetting, roughening, and second-order solid-gas transitions are found and discussed. The effects of further-neighbor interactions in adsorbates are analyzed at zero temperature and are found to play a crucial role in certain situations. Contact is made with experiment, and new experiments are proposed.