Background: Iberdomide is a novel cereblon E3 ligase modulator with enhanced tumouricidal and immune-stimulatory effects compared with immunomodulatory drugs. In preclinical myeloma models, iberdomide has shown synergy with dexamethasone, proteasome inhibitors, and CD38 monoclonal antibodies. We aimed to evaluate the safety and clinical activity of iberdomide plus dexamethasone in patients with heavily pretreated relapsed or refractory multiple myeloma. Methods: We conducted a multicohort, open-label, phase 1/2 trial (CC-220-MM-001) at 42 treatment centres in Europe, Canada, and the USA. Patients aged 18 years or older with multiple myeloma who had received at least two previous lines of therapy, including lenalidomide or pomalidomide and a proteasome inhibitor, were enrolled into the dose-escalation cohort. Patients received escalating doses of oral iberdomide (0·3–1·6 mg on days 1–21 of each 28-day cycle) plus oral dexamethasone (40 mg [20 mg if age >75 years] once per week). A dose-expansion cohort at the recommended phase 2 dose was planned for patients who had received at least three previous lines of therapy and had triple-class refractory disease (refractory to immunomodulatory drugs, proteasome inhibitors, and CD38 antibodies). Treatment continued until progressive disease or unacceptable toxicity. The primary outcomes were the recommended phase 2 dose (in the dose-escalation cohort, phase 1) and overall response rate (defined as complete response or partial response; in the dose-expansion cohort, phase 2) in the full analysis set. This trial is ongoing and is registered with ClinicalTrials.gov, NCT02773030. Findings: Between Dec 5, 2016, and Dec 16, 2020, 460 patients were assessed for eligibility across all cohorts and 197 were enrolled and treated with iberdomide plus dexamethasone (90 patients in the dose-escalation cohort and 107 in the dose-expansion cohort). In the dose-escalation cohort, 47 (52%) patients were female and 43 (48%) were male, 70 (78%) were White, and the median number of previous lines of therapy was 5 (IQR 4–8). In the dose-expansion cohort, 47 (44%) were female and 60 (56%) were male, 84 (79%) were White, and the median number of previous lines of therapy was 6 (IQR 5–8). At data cutoff (June 2, 2021), median follow-up was 5·8 months (IQR 3·0–13·7) in the dose-escalation cohort and 7·7 months (5·3–11·4) in the dose-expansion cohort. Two dose-limiting toxicities (both infections, at 1·2 mg and 1·3 mg) were observed in the dose-escalation cohort, and 1·6 mg was selected as the recommended phase 2 dose. In the dose-escalation cohort, the overall response rate was 32% (95% CI 23–43; 29 of 90 patients) across all doses, and the maximum tolerated dose was not reached. In the dose-expansion cohort, the overall response rate was 26% (95% CI 18–36; 28 of 107 patients). The most common grade 3 or worse adverse events were neutropenia (48 [45%] of 107 patients), anaemia (30 [28%]), infection (29 [27%]), and thrombocytopenia (23 [22%]). Serious adverse events occurred in 57 (53%) patients. There was one (1%) treatment-related death (sepsis) and five (5%) patients discontinued iberdomide due to adverse events. Interpretation: Iberdomide plus dexamethasone was generally safe and showed meaningful clinical activity in heavily pretreated patients with multiple myeloma, including in disease that was refractory to immunomodulatory drugs. These data suggest that further evaluation of iberdomide plus dexamethasone or other standard antimyeloma therapies is warranted. Funding: Bristol Myers Squibb.