We present a novel framework for the study of a large class of non-linear stochastic PDEs, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedom without resorting to any regularization scheme and to the subtraction of infinities. This talk is based on the article https://arxiv.org/pdf/2009.07640.pdf, joint work with C. Dappiaggi, N. Drago and P. Rinaldi.