Calcium plays an essential role in excitation-contraction coupling in muscle, and derangements in calcium handling can produce a variety of potentially harmful conditions, especially in cardiac muscle. In cardiac tissue, periodic invaginations of the membrane penetrate deep into each sarcomere, and depolarization of the membrane leads to an influx of calcium through voltage-sensitive channels in these invaginations. This in turn triggers further calcium release from intracellular stores via ryanodine-sensitive calcium channels. Under certain conditions cardiac cells release calcium from the sarcoplasmic reticulum spontaneously, producing a calcium ``spark'' and propagating traveling waves of elevated calcium, without depolarization of the membrane. However, under normal resting conditions these potentially harmful waves seldom occur. In this talk we discuss analytical and computational results which shed light on the role of the periodic distribution of ryanodine-sensitive channels in determining whether a spark can trigger a wave. We show that the periodic spatial localization of these channels has a significant effect on both wave propagation and the onset of oscillations in this system.