Every heartbeat is preceded by an electrical wave of excitation that rapidly propagates through the cardiac muscle, triggering mechanical contractions of cardiac myocytes. Abnormal propagation of this wave causes severe cardiac arrhythmias. The most dangerous of these is ventricular fibrillation, the leading cause of sudden death in the industrialized world. It is well established that ventricular fibrillation is a result of turbulent propagation of the electrical excitation wave. However, despite more than a century of investigation, the precise mechanism of its initiation and maintenance remains largely unknown. Novel experimental tools for the visualization of the excitation wave as well as advanced three–dimensional computer models of the heart, which have become available in recent years, have intensified attempts to solve the puzzle of ventricular fibrillation. These efforts have revealed significantly different manifestations of ventricular fibrillation, suggesting that multiple mechanisms are responsible for this arrhythmia. Several new hypotheses have been put forward recently that deviate considerably from Moe's standard hypothesis of fibrillation, which has dominated the field for almost four decades. One of the hypotheses that has been most actively discussed is the spiral–breakup (also called the restitution) hypothesis. This hypothesis may lead to a breakthrough in our understanding of the factors that cause this deadly arrhythmia and provide a constructive approach to the development of efficient antifibrillatory drugs.