Sequence-specific nucleases have been applied to engineer targeted modifications in polyploid genomes¹, but simultaneous modification of multiple homoeoalleles has not been reported. Here we use transcription activator–like effector nuclease (TALEN)^{2, 3} and clustered, regularly interspaced, short palindromic repeats (CRISPR)-Cas9 (refs. 4,5) technologies in hexaploid bread wheat to introduce targeted mutations in the three homoeoalleles that encode MILDEW-RESISTANCE LOCUS (MLO) proteins⁶. Genetic redundancy has prevented evaluation of whether mutation of all three MLO alleles in bread wheat might confer resistance to powdery mildew, a trait not found in natural populations⁷. We show that TALEN-induced mutation of all three TaMLO homoeologs in the same plant confers heritable broad-spectrum resistance to powdery mildew. We further use CRISPR-Cas9 technology to generate transgenic wheat plants that carry mutations in the TaMLO-A1 allele. We also demonstrate the feasibility of engineering targeted DNA insertion in bread wheat through nonhomologous end joining of the double-strand breaks caused by TALENs. Our findings provide a methodological framework to improve polyploid crops.