The boundary of melting ice forms a random interface. So does the frontier of slowing burning pieces of paper. As time changes, the interface evolves in a random fashion. In probability theory, a collection of models often exhibits universal behaviors when the system size or time becomes large. The KPZ universality class comprises 1+1 dimensional probability models that mimic the random growth behavior mentioned above and display particular universal fluctuations. We will overview some of the development in this class that started about two decades ago. Speaker(s): Jinho Baik (University of Michigan)