Modern faces of filtration Johan van Benthem, Nick Bezhanishvili Abstract: The filtration method for proving decidability in a focused minimal manner is a highlight of modal logic, widely used, but also posing a bit of a challenge as to its scope and what makes it tick. In this paper, we bring together a number of modern perspectives on filtration, including model-theoretic and proof-theoretic ones. We also include a few more unusual recent connections with dynamic logics of model change and logics of issues. Finally, we analyze where the filtration method fails in full first-order logic, and what is still has to say there.