Three decades ago, Stanley and Brenti initiated the study of the Kazhdan–Lusztig–Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In this talk we will introduce new polynomial functions called Chow functions associated to any graded bounded poset and study their applications to matroid theory, polytopes and Coxeter groups. The Chow functions often exhibit remarkable properties (positivity, palindromicity, unimodality, gamma-positivity), and sometimes encode the graded dimensions of a cohomology or Chow ring. One of the best features of this general framework is that unimodality statements can be proven for posets without relying on versions of the Hard Lefschetz theorem. Our framework shows that there is an unexpected relation between positivity and real-rootedness conjectures about chains on face lattices of polytopes by Brenti and Welker, Hilbert–Poincaré series of matroid Chow rings by Ferroni and Schröter, and flag enumerations on Bruhat intervals of Coxeter groups by Billera and Brenti. This is joint work with Luis Ferroni and Jacob Matherne.