The notion of strong stationarity was introduced by Furstenberg and Katznelson in the early 90's in order to facilitate the proof of the density Hales-Jewett theorem. It has recently surfaced that this strong statistical property is shared by several natural sequences. I will explain how one can exploit this unexpected feature in order to give nontrivial results about correlations of the Liouville and other multiplicative functions. In the course of the lecture I will also give a (gentle I hope) introduction to Furstenberg systems of bounded sequences.