  We study Gr\"obner degenerations of Schubert varieties inside flag varieties.
We consider toric degenerations of flag varieties induced by matching fields
and semi-standard Young tableaux. We describe an analogue of matching field
ideals for Schubert varieties inside the flag variety and give a complete
characterization of toric ideals among them. We use a combinatorial approach to
standard monomial theory to show that block diagonal matching fields give rise
to toric degenerations. Our methods and results use the combinatorics of
permutations associated to Schubert varieties, matching fields and their
corresponding tableaux.
