At 3, 6 and 12 months from the index procedure a complete follow-up visit is performed for all patients in both study arms. Clinical assessment will include signs and symptoms of heart failure, NYHA functional class evaluation, quality of life assessment by MLWHF questionnaire and a 12-lead ECG. Additionally, all patients will undergo a complete transthoracic echocardiographic evaluation, including LV ejection fraction, end-diastolic and end-systolic volumes, LV diastolic function, LA volume, mitral regurgitation or stenosis grade, right ventricular diameter and systolic function (TAPSE). A 6-minute walking test will be performed aiming to reproducibly quantify the functional class of the patients at each scheduled evaluation. A 24-hour ECG Holter will be performed in all patients, to detect AF recurrences in the AF ablation arm, mean heart rate (both for patients in AF and SR) and ventricular arrhythmias burden. For patients implanted with a device, AF burden, ICD interventions and percentage of biventricular pacing will be recorded. Finally, the incidence of heart failure hospitalizations, ischemic or hemorrhagic strokes and all-cause mortality will be assessed in both groups. Additional clinical assessment will be performed in case of heart failure acute worsening.