In this talk we explain recent results relating the six-vertex model and the Kardar-Parisi-Zhang (KPZ) universality class. In particular, we describe how the six-vertex model can be used to analyze stochastic interacting particle systems, such as asymmetric exclusion processes, and how infinite-volume pure states of the ferroelectric six-vertex model exhibit fluctuations of order N^{1/3}, a characteristic feature of systems in the KPZ universality class.