I will motivate the study of the Schubert variety of a pair of linear spaces via Kempf collapsing of vector bundles. I'll describe equations defining this variety and how this yields a simplicial complex determined by a pair of matroids which generalizes the Schubert variety of the pair of linear spaces.Toward the end of the talk, I'll discuss how one extends the most interesting properties of the variety to arbitrary pairs of matroids, yielding some beautiful positivity results.