Of all the features of the electrocardiogram, the T wave shows the earliest and most dramatic correlation with abnormalities of electrical behavior in the heart. Yet, it has remained difficult to make quantitative connections between the T wave and electrical activity in the heart at the cellular level. It is the purpose of this paper to review attempts at deriving T waves from a knowledge of the membrane electrical activity in the heart and the geometry and conductive properties of the heart and its surrounding medium. We first summarize the problem of calculating T-wave potentials on the body surface, based on physical laws. Next, we review the empirical conclusions that have been reached through observations of the T wave, including its connection with repolarization of the cell membrane, the distributed nature of the current source during the T wave, and the gradient in action potential duration responsible for the positive polarity of the normal T wave. Six quantitative models have been proposed for the T wave; we compare these models and comment on their accuracy and underlying assumptions. Finally, we discuss ideas that have been suggested for the membrane mechanism of repolarization and the T wave.