The Taylor-Wiles method, and its more elaborate variants due to Faltings, Fujiwara, Diamond, and Kisin, has been used in a variety of situations to prove that p-adic Galois representations are attached to automorphic forms. The method was developed in the setting of elliptic modular forms, or of automorphic forms on totally definite unitary groups, in order to avoid complications arising from torsion in cohomology. A recent vanishing theorem of Lan and Suh makes it possible to apply the Taylor-Wiles method to coherent cohomology and p-adic de Rham and \´etale cohomology of certain Shimura varieties. The method does not yield new modularity results, but it does show that these cohomology groups tend to be free over Hecke algebras, after localization at a non-Eisenstein prime.