The discovery by Fujita and Li of a valuative characterization of K-stability for Fano varieties has played a key role in the fantastic progress accomplished over the last few years in this field. The goal of this talk is to discuss a version of this valuative criterion for general polarized varieties, which characterizes (uniform) K-stability with respect to filtrations, itself implying the existence of a cscK metric thanks to Chi Li's recent breakthrough. This is joint work with Mattias Jonsson.