The development of new observational, experimental, and computational technologies is changing our understanding of the origins of the elements by thermonuclear burning in stars. Gamma-ray lines from newly made radioactive nuclei have been identified using instruments onboard low-Earth orbiting satellites. Grains in meteorites have isotopic anomalies which suggest that the grains were put together in a stellar explosion such as a supernova. Computer simulations allow such anomalies to be used to probe how these events happen. The simulations are being independently tested by experiments with high-energy density lasers, These developments are beginning to provide a quantitative diagnostic of galactic evolution, and of the epoch of formation of the first stars and galaxies.