New statistical descriptions related to the so-called Scattering Transform recently obtained attractive results for several astrophysical applications. These statistics share ideas with convolutional neural networks, but do not require to be learned, allowing for a direct characterization of interactions between scales in non-linear processes. In this talk, I will introduce these statistical descriptions, and give an overview of the different results obtained recently. I will focus in particular on the ongoing work about components separation, in particular in the scientific context of CMB B-modes detection beyond the Galactic foreground emission.