The probabilistic study of effective interface models has been quite active in recent years, with a particular emphasis on the effect of various external potentials (wall, pinning potential, ...) leading to localization/delocalization transitions. I review some of the results that have been obtained. In particular, I discuss pinning by a local potential, entropic repulsion and the (pre)wetting transition, both for models with continuous and discrete heights.
"Localization and delocalization of random interfaces." Probab. Surveys 3 112 - 169, 2006. https://doi.org/10.1214/154957806000000050