We formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable, given by a Wiener chaos expansion over the d-dimensional white noise. This provides a unified framework to study the continuum and weak disorder scaling limits of statistical mechanics systems that are disorder relevant, including the disordered pinning model with renewal exponent between 1/2 and 1, the (long-range) directed polymer model in dimension 1+1, and the two-dimensional random field Ising model. This gives a new perspective in the study of disorder relevance, and leads to interesting new continuum models. However, this approach breaks down for systems where the disorder is marginally relevant, such as the disordered pinning model with renewal exponent 1/2, and the directed polymer model in dimension 2+1. Nevertheless, we show that a scaling limit still exists, and is furthermore universal across the different models. Joint work with Francesco Caravenna and Nikos Zygouras.