Ventricular fibrillation (VF) remains a major cause of death in the industrialized world. Alternans (a period-doubling bifurcation of cardiac electrical activity) have recently been causally linked to the progression from ventricular tachycardia (VT) to VF, a more spatiotemporally disorganized electrical activity. In this paper, we show how alternans and thus VT degenerate to chaos via multiple, specific dynamical routes, largely associated with spatial components of VF dynamics, explaining failures of many recently proposed antiarrhythmic drugs. Identification of dynamical mechanisms for the onset of VF should lead to the design of future experiments and consequently to more effective antiarrhythmic drugs.