The groundbreaking results by Huh (further extended in joint work with Adiprasito and Katz) allowed to associate to a matroid a class in the Chow ring of the permutohedral variety. The technique turned out to be especially powerful, as certain invariants of the matroid could be expressed as intersection products in this Chow ring. Can this technique be used further, beyond matroids and the permutohedral variety?We will point out very explicit analogies of the work of Huh and Schubert. This will bring us to applications e.g. in statistics, through maximum likelihood degree. Finally, we will go back to combinatorics, presenting closed formulas for mixed Eulerian numbers.