BACKGROUND: The optimal rhythm management strategy for people with non-paroxysmal (persistent or long-standing persistent) atrial fibrilation is currently not well defined. Antiarrhythmic drugs have been the mainstay of therapy. But recently, in people who have not responded to antiarrhythmic drugs, the use of ablation (catheter and surgical) has emerged as an alternative to maintain sinus rhythm to avoid long-term atrial fibrillation complications. However, evidence from randomised trials about the efficacy and safety of ablation in non-paroxysmal atrial fibrillation is limited. OBJECTIVES: To determine the efficacy and safety of ablation (catheter and surgical) in people with non-paroxysmal (persistent or long-standing persistent) atrial fibrillation compared to antiarrhythmic drugs. SEARCH METHODS: We searched the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE Ovid, Embase Ovid, conference abstracts, clinical trial registries, and Health Technology Assessment Database. We searched these databases from their inception to 1 April 2016. We used no language restrictions. SELECTION CRITERIA: We included randomised trials evaluating the effect of radiofrequency catheter ablation (RFCA) or surgical ablation compared with antiarrhythmic drugs in adults with non-paroxysmal atrial fibrillation, regardless of any concomitant underlying heart disease, with at least 12 months of follow-up. DATA COLLECTION AND ANALYSIS: Two review authors independently selected studies and extracted data. We evaluated risk of bias using the Cochrane 'Risk of bias' tool. We calculated risk ratios (RRs) for dichotomous data with 95% confidence intervals (CIs) a using fixed-effect model when heterogeneity was low (I² <= 40%) and a random-effects model when heterogeneity was moderate or substantial (I² > 40%). Using the GRADE approach, we evaluated the quality of the evidence and used the GRADE profiler (GRADEpro) to import data from Review Manager 5 to create 'Summary of findings' tables. MAIN RESULTS: We included three randomised trials with 261 participants (mean age: 60 years) comparing RFCA (159 participants) to antiarrhythmic drugs (102) for non-paroxysmal atrial fibrillation. We generally assessed the included studies as having low or unclear risk of bias across multiple domains, with reported outcomes generally lacking precision due to low event rates. Evidence showed that RFCA was superior to antiarrhythmic drugs in achieving freedom from atrial arrhythmias (RR 1.84, 95% CI 1.17 to 2.88; 3 studies, 261 participants; low-quality evidence), reducing the need for cardioversion (RR 0.62, 95% CI 0.47 to 0.82; 3 studies, 261 participants; moderate-quality evidence), and reducing cardiac-related hospitalisation (RR 0.27, 95% CI 0.10 to 0.72; 2 studies, 216 participants; low-quality evidence) at 12 months follow-up. There was substantial uncertainty surrounding the effect of RFCA regarding significant bradycardia (or need for a pacemaker) (RR 0.20, 95% CI 0.02 to 1.63; 3 studies, 261 participants; low-quality evidence), periprocedural complications, and other safety outcomes (RR 0.94, 95% CI 0.16 to 5.68; 3 studies, 261 participants; very low-quality evidence). AUTHORS' CONCLUSIONS: In people with non-paroxysmal atrial fibrillation, evidence suggests a superiority of RFCA to antiarrhythmic drugs in achieving freedom from atrial arrhythmias, reducing the need for cardioversion, and reducing cardiac-related hospitalisations. There was uncertainty surrounding the effect of RFCA with significant bradycardia (or need for a pacemaker), periprocedural complications, and other safety outcomes. Evidence should be interpreted with caution, as event rates were low and quality of evidence ranged from moderate to very low.