the growth of random surfaces has attracted a lot of attention in probability theory in the last ten years, especially in the context of the kardar-parisi-zhang (kpz) equation. most of the available results are for exactly solvable one-dimensional models. in this talk i will present some recent results for models that are not exactly solvable. in particular, i will talk about the universality of deterministic kpz growth in arbitrary dimensions, and if time permits, a necessary and sufficient condition for superconcentration in a class of growing random surfaces.