Gamma-ray spectroscopy holds great promise for probing nucleosynthesis in individual supernova explosions via short-lived radioactivity, and for measuring current global Galactic supernova nucleosynthesis with longer-lived radioactivity. It was somewhat surprising that the former case was realized first for a Type II supernova, when both Co-56 and Co-57 were detected in SN 1987A. These provide unprecedented constraints on models of Type II explosions and nucleosynthesis. Live Al-26 in the Galaxy might come from Type II supernovae, and if it is eventually shown to be so, can constrain massive star evolution, supernova nucleosynthesis, and the Galactic Type II supernova rate. Type Ia supernovae, thought to be thermonuclear explosions, have not yet been detected in gamma-rays. This is somewhat surprising given current models and recent Co-56 detection attempts. Ultimately, gamma-ray measurements can confirm their thermonuclear nature, probe the nuclear burning conditions, and help evaluate their contributions to Galactic nucleosynthesis. Type Ib/c supernovae are poorly understood. Whether they are core collapse or thermonuclear events might be ultimately settled by gamma-ray observations. Depending on details of the nuclear processing, any of these supernova types might contribute to a detectable diffuse glow of Fe-60 gamma-ray lines. Previous attempts at detection have come very close to expected emission levels. Remnants of any type of age less that a few centuries might be detectable as individual spots of Ti-44 gamma-ray line emission. It is in fact quite surprising that previous surveys have not discovered such spots, and the constraints on the combination of nucleosynthesis yields and supernova rates are very interesting. All of these interesting limits and possibilities mean that the next mission, International Gamma-Ray Astrophysics Laboratory (INTEGRAL), if it has sufficient sensitivity, is very likely to lead to the realization of much of the great potential of gamma-ray spectroscopy for understanding supernovae