AZD5153, a reversible, bivalent inhibitor of the bromodomain and extraterminal family protein BRD4, has preclinical activity in multiple tumors. This first-in-human, phase I study investigated AZD5153 alone or with olaparib in patients with relapsed/refractory solid tumors or lymphoma. Adults with relapsed tumors intolerant of, or refractory to, prior therapies received escalating doses of oral AZD5153 once daily or twice daily continuously (21-day cycles), or AZD5153 once daily/twice daily continuously or intermittently plus olaparib 300 mg twice daily, until disease progression or unacceptable toxicity. Between June 30, 2017 and April 19, 2021, 34 patients received monotherapy and 15 received combination therapy. Dose-limiting toxicities were thrombocytopenia/platelet count decreased (n = 4/n = 2) and diarrhea (n = 1). The recommended phase II doses (RP2D) were AZD5153 30 mg once daily or 15 mg twice daily (monotherapy) and 10 mg once daily (intermittent schedule) with olaparib. With AZD5153 monotherapy, common treatment-emergent adverse events (TEAE) included fatigue (38.2%), thrombocytopenia, and diarrhea (each 32.4%); common grade ≥ 3 TEAEs were thrombocytopenia (14.7%) and anemia (8.8%). With the combination, common TEAEs included nausea (66.7%) and fatigue (53.3%); the most common grade ≥ 3 TEAE was thrombocytopenia (26.7%). AZD5153 had dose-dependent pharmacokinetics, with minimal accumulation, and demonstrated dose-dependent modulation of peripheral biomarkers, including upregulation of HEXIM1. One patient with metastatic pancreatic cancer receiving combination treatment had a partial response lasting 4.2 months. These results show AZD5153 was tolerable as monotherapy and in combination at the RP2Ds; common toxicities were fatigue, hematologic AEs, and gastrointestinal AEs. Strong evidence of peripheral target engagement was observed.