Mesothelioma is a rare and fatal cancer with limited therapeutic options until the recent approval of combination immune checkpoint blockade. Here we report the results of the phase 2 PrE0505 trial ( NCT02899195 ) of the anti-PD-L1 antibody durvalumab plus platinum-pemetrexed chemotherapy for 55 patients with previously untreated, unresectable pleural mesothelioma. The primary endpoint was overall survival compared to historical control with cisplatin and pemetrexed chemotherapy; secondary and exploratory endpoints included safety, progression-free survival and biomarkers of response. The combination of durvalumab with chemotherapy met the pre-specified primary endpoint, reaching a median survival of 20.4 months versus 12.1 months with historical control. Treatment-emergent adverse events were consistent with known side effects of chemotherapy, and all adverse events due to immunotherapy were grade 2 or lower. Integrated genomic and immune cell repertoire analyses revealed that a higher immunogenic mutation burden coupled with a more diverse T cell repertoire was linked to favorable clinical outcome. Structural genome-wide analyses showed a higher degree of genomic instability in responding tumors of epithelioid histology. Patients with germline alterations in cancer predisposing genes, especially those involved in DNA repair, were more likely to achieve long-term survival. Our findings indicate that concurrent durvalumab with platinum-based chemotherapy has promising clinical activity and that responses are driven by the complex genomic background of malignant pleural mesothelioma.