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Matroids appear naturally in algebraic geometry in correspondence to toric varieties for a canonical torus action on the Grassmannian. For a similar torus action on certain flag varieties, Borovik, Gelfand, Vince, and White showed that the orbits correspond to an analogous combinatorial object called underlying flag matroids. In this talk, I will discuss a generalization of underlying flag matroids to polymatroids, describe its combinatorics completely, and describe how this generalization is informed by geometry. As a consequence, we show a new description of the combinatorics of underlying flag matroids that in particular implies toric varieties corresponding to underlying flag matroids are always smooth. Based on joint work with Raman Sanyal.