Alternation of cardiac action potential duration from beat to beat and concurrent alternation of the amplitude of the calcium transient are both regarded as important arrhythmia mechanisms. These phenomena are causally interrelated and can be reliably evoked by an increase in beat frequency or by ischemia. This paper is intended as a historical review. The first part of the review deals with the physiology of APD alternans. Sections recounting the evolution of knowledge about calcium activated ion currents and calcium transient alternans are interspersed among sections describing the growth of the so called "restitution hypothesis" which involves time-dependent recovery of the potassium channels (including their passage through pre-open states) as a function of diastolic interval. Major developments are generally in chronological order, but it is necessary to move back and forth between the two theories in order to respect the overall timeline which runs from about 1965 to the present. The concluding two sections deal with the pathophysiology of calcium transient and APD alternans during ischemia, which may be the basis for out of hospital cardiac arrest during the initial stages of acute myocardial infarction.