T-wave alternans, a powerful marker for the risk of sudden cardiac death is directly related to alternans of the cellular action potential. When action potential alternans is first initiated, it occurs with identical phase in all cells of a particular region of the heart. However, above a critical heart rate threshold, action potential alternans switches phase in some cells but not in others, such that some cells undergo a prolongation of action potential duration (APD), whereas neighbouring cells undergo APD shortening on the same beat (i.e. discordant alternans). Discordant alternans is linked to a mechanism of arrhythmogenesis because when ventricular action potentials from neighbouring cells are alternating out of phase, repolarization gradients are amplified, producing conduction block and re-entrant excitation. In this review, we discuss potential mechanisms which may underlie discordant alternans in the heart, including (i) conduction velocity restitution, (ii) spatial heterogeneities of calcium cycling and the sarcolemmal ionic currents which govern repolarization, and (iii) intercellular uncoupling.