Atrial fibrillation (AF) is the most common sustained arrhythmia in clinical practice. Its prevalence is increasing in our ageing population, and it has a soaring impact on health systems. It can cause thrombo-embolism, heart failure, and hospitalizations, and is associated with a two-fold increase in all-cause mortality. There have been great advances in understanding the mechanism of AF that are currently being translated into new therapeutic concepts. Experimental studies demonstrated that AF-induced electrical and structural remodelling of the fibrillating atria perpetuate AF ('AF begets AF'). Furthermore, there is growing understanding that the atria are an endocrine organ expressing angiotensin and thrombogenic substances. Clinical, electrophysiological studies have identified automatic triggers, often in the pulmonary veins, that initiate paroxysmal AF. Electrical isolation of the pulmonary veins by circular ablation abolishes these triggers. Whereas isolation of the pulmonary veins often maintains sinus rhythm in patients with paroxysmal AF, additional ablation strategies are used in persistent and permanent AF to modify the more complex electrical and structural atrial changes. The 'role model' for extensive ablation in the left atrium is the surgical MAZE procedure that abolishes long-standing AF by cutting and sewing the atria into complex pieces. New surgical approaches of AF therapy use radiofrequency or other sources for an easy ablation during open-heart surgery. A lot of effort has also been put in the development of device therapy for the treatment of AF, with mixed effects on maintenance of sinus rhythm, but unexpected insights into the development of asymptomatic AF recurrences. This review aims to provide an overview of these non-pharmacological treatment options of AF in the context of potential pathophysiological processes.