Trabectedin is an alkylating drug with a unique mechanism of action causing single-strand and double-strand DNA breaks that activate DNA damage-response pathways. Based on our preclinical data, we hypothesised that poly(ADP-ribose) polymerase 1 (PARP1) inhibitors might be an ideal partner of trabectedin and aimed to assess the safety, identify the recommended phase 2 dose, and explore preliminary signs of activity of trabectedin and olaparib combination treatment in patients with bone and soft-tissue sarcoma. We did an open-label, multicentre, phase 1b study, recruiting patients from the national Italian sarcoma network aged 18 years and older with histologically confirmed bone and soft-tissue sarcoma progressing after standard treatments with Eastern Cooperative Oncology Group performance status of 1 or less. In a classic 3 + 3 design, patients received a 24 h infusion of trabectedin on day 1 and olaparib orally twice a day in 21-day cycles across six dose levels (trabectedin 0·675-1·3 mg/m every 3 weeks; olaparib 100-300 mg twice a day from day 1 to 21). Intermediate dose levels were permitted to improve safety and tolerability. The primary endpoint was determination of the recommended phase 2 dose (the maximum tolerated dose). Safety and antitumour activity were assessed in all patients who received at least one dose of the study drugs. We report the results of the dose-escalation and dose-expansion cohorts. The trial is still active but closed to enrolment, and follow-up for patients who completed treatment is ongoing. This trial is registered with ClinicalTrials.gov, number NCT02398058. Between Nov 17, 2014, and Jan 30, 2017, of 54 patients assessed for eligibility, we enrolled 50 patients: 28 patients in the dose-escalation cohort and 22 patients in the dose-expansion cohort. Patients received a median of four cycles of treatment (IQR 2-6; range 1-17 [the patients who received the highest number of cycles are still on treatment]) with a median follow-up of 10 months (IQR 5-23). Considering all dose levels, the most common grade 3-4 adverse events were lymphopenia (32 [64%] of 50 patients), neutropenia (31 [62%]), thrombocytopenia (14 [28%]), anaemia (13 [26%]), hypophosphataemia (20 [40%]), and alanine aminotransferase concentration increase (9 [18%]). No treatment-related life-threatening adverse events or deaths occurred. One (2%) patient interrupted treatment without progression without reporting any specific toxicity. Observed dose-limiting toxicities were thrombocytopenia, neutropenia for more than 7 days, and febrile neutropenia. We selected intermediate dose level 4b (trabectedin 1·1 mg/m every 3 weeks plus olaparib 150 mg twice a day) as the recommended phase 2 dose. Seven (14%; 95% CI 6-27) of 50 patients achieved a partial response according to Response Evaluation Criteria In Solid Tumors 1.1. Trabectedin and olaparib in combination showed manageable toxicities at active dose levels for both drugs. Preliminary data on antitumour activity are encouraging. Two dedicated phase 2 studies are planned to assess activity of this combination in both ovarian cancer (EudraCT2018-000230-35) and soft-tissue sarcomas. Italian Association for Cancer Research, Italian Sarcoma Group, Foundation for Research on Musculoskeletal and Rare Tumors, and Italian Ministry of Health.