Major electrophysiological mechanisms underlying atrial fibrillation were described around 100 years ago, but important recent improvements in biophysical theory, mapping of cardiac electric activity, and noninvasive imaging have generated significant new and controversial ideas. Here, we discuss these ideas, the evidence on which they are based, their significance for arrhythmia research and therapy, and the common underlying molecular mechanisms that may allow for therapeutic improvements even without definitive resolution of the electric processes that maintain atrial fibrillation.