Background: Mantle-cell lymphoma is an aggressive B-cell lymphoma with a poor prognosis. Both ibrutinib and temsirolimus have shown single-agent activity in patients with relapsed or refractory mantle-cell lymphoma. We undertook a phase 3 study to assess the efficacy and safety of ibrutinib versus temsirolimus in relapsed or refractory mantle-cell lymphoma. Methods: This randomised, open-label, multicentre, phase 3 clinical trial enrolled patients with relapsed or refractory mantle-cell lymphoma confirmed by central pathology in 21 countries who had received one or more rituximab-containing treatments. Patients were stratified by previous therapy and simplified mantle-cell lymphoma international prognostic index score, and were randomly assigned with a computer-generated randomisation schedule to receive daily oral ibrutinib 560 mg or intravenous temsirolimus (175 mg on days 1, 8, and 15 of cycle 1; 75 mg on days 1, 8, and 15 of subsequent 21-day cycles). Randomisation was balanced by using randomly permuted blocks. The primary efficacy endpoint was progression-free survival assessed by a masked independent review committee with the primary hypothesis that ibrutinib compared with temsirolimus significantly improves progression-free survival. The analysis followed the intention-to-treat principle. The trial is ongoing and is registered with ClinicalTrials.gov (number NCT01646021) and with the EU Clinical Trials Register, EudraCT (number 2012-000601-74). Findings: Between Dec 10, 2012, and Nov 26, 2013, 280 patients were randomised to ibrutinib (n=139) or temsirolimus (n=141). Primary efficacy analysis showed significant improvement in progression-free survival (p<0·0001) for patients treated with ibrutinib versus temsirolimus (hazard ratio 0·43 [95% CI 0·32-0·58]; median progression-free survival 14·6 months [95% CI 10·4-not estimable] vs 6·2 months [4·2-7·9], respectively). Ibrutinib was better tolerated than temsirolimus, with grade 3 or higher treatment-emergent adverse events reported for 94 (68%) versus 121 (87%) patients, and fewer discontinuations of study medication due to adverse events for ibrutinib versus temsirolimus (9 [6%] vs 36 [26%]). Interpretation: Ibrutinib treatment resulted in significant improvement in progression-free survival and better tolerability versus temsirolimus in patients with relapsed or refractory mantle-cell lymphoma. These data lend further support to the positive benefit-risk ratio for ibrutinib in relapsed or refractory mantle-cell lymphoma. Funding: Janssen Research & Development, LLC.