The Minimizing Adverse Haemorrhagic Events by Transradial Access Site and Systemic Implementation of Angiox (MATRIX) programme was designed to assess the comparative safety and effectiveness of radial versus femoral access and of bivalirudin versus unfractionated heparin with optional glycoprotein IIb/IIIa inhibitors in patients with the whole spectrum of acute coronary syndrome undergoing invasive management. Here we describe the prespecified final 1-year outcomes of the entire programme. MATRIX was a programme of three nested, randomised, multicentre, open-label, superiority trials in patients with acute coronary syndrome in 78 hospitals in Italy, the Netherlands, Spain, and Sweden. Patients with ST-elevation myocardial infarction were simultaneously randomly assigned (1:1) before coronary angiography to radial or femoral access and to bivalirudin, with or without post-percutaneous coronary intervention infusion or unfractionated heparin (one-step inclusion). Patients with non-ST-elevation acute coronary syndrome were randomly assigned (1:1) before coronary angiography to radial or femoral access and, only if deemed eligible to percutaneous coronary intervention after angiography (two-step inclusion), entered the antithrombin type and treatment duration programmes. Randomisation sequences were computer generated, blocked, and stratified by intended new or current use of P2Y12 inhibitor (clopidogrel vs ticagrelor or prasugrel), and acute coronary syndrome type (ST-elevation myocardial infarction, troponin-positive, or troponin-negative non-ST-elevation acute coronary syndrome). Bivalirudin was given as a bolus of 0·75 mg/kg, followed immediately by an infusion of 1·75 mg/kg per h until completion of percutaneous coronary intervention. Heparin was given at 70-100 units per kg in patients not receiving glycoprotein IIb/IIIa inhibitors, and at 50-70 units per kg in patients receiving glycoprotein IIb/IIIa inhibitors. Clinical follow-up was done at 30 days and 1 year. Co-primary outcomes for MATRIX access and MATRIX antithrombin type were major adverse cardiovascular events, defined as the composite of all-cause mortality, myocardial infarction, or stroke up to 30 days; and net adverse clinical events, defined as the composite of non-coronary artery bypass graft-related major bleeding, or major adverse cardiovascular events up to 30 days. The primary outcome for MATRIX treatment duration was the composite of urgent target vessel revascularisation, definite stent thrombosis, or net adverse clinical events up to 30 days. Analyses were done according to the intention-to-treat principle. This trial is registered with ClinicalTrials.gov, number NCT01433627. Between Oct 11, 2011, and Nov 7, 2014, we randomly assigned 8404 patients to receive radial (4197 patients) or femoral (4207 patients) access. Of these 8404 patients, 7213 were included in the MATRIX antithrombin type study and were randomly assigned to bivalirudin (3610 patients) or heparin (3603 patients). Patients assigned to bivalirudin were included in the MATRIX treatment duration study, and were randomly assigned to post-procedure infusion (1799 patients) or no post-procedure infusion (1811 patients). At 1 year, major adverse cardiovascular events did not differ between patients assigned to radial access compared with those assigned to femoral access (14·2% vs 15·7%; rate ratio 0·89, 95% CI 0·80-1·00; p=0·0526), but net adverse clinical events were fewer with radial than with femoral access (15·2% vs 17·2%; 0·87, 0·78-0·97; p=0·0128). Compared with heparin, bivalirudin was not associated with fewer major adverse cardiovascular (15·8% vs 16·8%; 0·94, 0·83-1·05; p=0·28) or net adverse clinical events (17·0% vs 18·4%; 0·91, 0·81-1·02; p=0·10). The composite of urgent target vessel revascularisation, stent thrombosis, or net adverse clinical events did not differ with or without post-procedure bivalirudin infusion (17·4% vs 17·4%; 0·99, 0·84-1·16; p=0·90). In patients with acute coronary syndrome, radial access was associated with lower rates of net adverse clinical events compared with femoral access, but not major adverse cardiovascular events at 1 year. Bivalirudin with or without post-procedure infusion was not associated with lower rates of major adverse cardiovascular events or net adverse clinical events. Radial access should become the default approach in acute coronary syndrome patients undergoing invasive management. Italian Society of Invasive Cardiology, The Medicines Company, Terumo, amd Canada Research Chairs Programme.