Polynomial chaos refers to a polynomial function evaluated on a sequence of i.i.d. random variables. These objects arise naturally in a wide range of probabilistic models — including random graphs, spin glass systems, and random matrix theory, just to name a few. They constitute a powerful and flexible framework, particularly for the polynomial approximation of general random fields. In this talk, we characterize all possible limits of sequences of polynomial chaoses with uniformly bounded degrees, thereby resolving a longstanding open question in the field. After presenting several natural settings in which such structures appear, we will outline key applications of our results and provide an overview of the main ideas behind the proofs\