Title: KPZ limit theorems

Abstract: One-dimensional interacting particle systems, 1+1 random growth models, and two-dimensional directed polymers define two-dimensional random fields. The KPZ universality conjectures that an appropriately scaled height function converges to a model-independent universal random field for a large class of models. We survey some of the limit theorems and discuss changes that arise when we consider different domains. In particular, we present recent results on periodic domains. We also comment on integrable probability models, integrable differential equations, and universality.