The complete flag variety FL_n is a central object in combinatorial algebraic geometry, parametrizing maximal chains of vector subspaces. One can discover many of its algebro-geometric features by flatly degenerating it to a projective toric variety—a combinatorial shadow carrying rich information about the original space. A SAGBI basis (the "subalgebra analogue of Gröbner basis for ideals") guarantees such a toric degeneration. In this talk, we will compute an explicit SAGBI basis for the multi-homogeneous coordinate ring of FL_n called the Plücker algebra, and connect it to other well-studied combinatorial semigroups.