In this talk various results will be discussed on global fluctuations for point processes from random matrix theory and related models. In recent years it has been shown that such fluctuations in various cases are governed by the Gaussian Free Field. This remarkable connection has sparked new interest and activity. The purpose of the talk is to present an introduction to the topic for a broad audience and discuss various important historic results. The discussion will be centered around a particular class of models involving non-colliding processes. If time permits, we will also briefly discuss a new approach for determinantal point processes.
