Genetically engineered T cell therapy can induce remarkable tumor responses in hematologic malignancies. However, it is not known if this type of therapy can be applied effectively to epithelial cancers, which account for 80–90% of human malignancies. We have conducted a first-in-human, phase 1 clinical trial of T cells engineered with a T cell receptor targeting HPV-16 E7 for the treatment of metastatic human papilloma virus-associated epithelial cancers (NCT02858310). The primary endpoint was maximum tolerated dose. Cell dose was not limited by toxicity with a maximum dose of 1 × 10¹¹ engineered T cells administered. Tumor responses following treatment were evaluated using RECIST (Response Evaluation Criteria in Solid Tumors) guidelines. Robust tumor regression was observed with objective clinical responses in 6 of 12 patients, including 4 of 8 patients with anti-PD-1 refractory disease. Responses included extensive regression of bulky tumors and complete regression of most tumors in some patients. Genomic studies, which included intra-patient tumors with dichotomous treatment responses, revealed resistance mechanisms from defects in critical components of the antigen presentation and interferon response pathways. These findings demonstrate that engineered T cells can mediate regression of common carcinomas, and they reveal immune editing as a constraint on the curative potential of cellular therapy and possibly other immunotherapies in advanced epithelial cancer.