Reentrant tachycardias are abnormally fast cardiac rhythms produced by the circulation of electrical activity around some anatomical obstacle in the heart, or by spiral wave rotation around a phase singularity in homogeneous tissue. These arrhythmia are especially dangerous because they can become unstable and decay into fibrillation, a wave turbulent state that destroys the main pumping function of the heart if present in the ventricle. I will discuss the results of a modeling study aimed at controlling a known oscillatory instability of reentrant excitations in both one-dimensional rings and thin two-dimensional sheets of tissue. The good news is that control can be achieved, and the decay into turbulence prevented, with a relatively small number of spatially distributed pacing electrodes and a relatively simple control scheme. The bad news, however, is that ventricular fibrillation can also be produced by a distinct three-dimensional instability of scroll wave filaments that would require a completely different control strategy, yet to be developed.