Nuclear reactions occur in cosmic environments in the cores of stars and in stellar explosions. Nuclear energy production is a key agent in these objects; the production of new isotopes drives the chemical evolution of gas throughout the universe and of the objects which form from this gas over cosmic times. Radioactive isotopes, ejected into interstellar space by cosmic nucleosynthesis events, are observed with new space telescopes. Gamma-ray lines from the radioactive ejecta of such cosmic nuclear reactors need to be sufficiently bright so they can be observed with current telescopes; this limits all gamma-ray astronomy studies to present and nearby nucleosynthesis processes, i.e. out to few Mpc in distance and back a few million years in time. The Compton Observatory had provided a first sky survey for the isotopes 56Co, 22Na, 44Ti, and 26Al, detecting supernova radioactivity and the diffuse glow of long-lived radioactivity from massive stars in the Galaxy. High-resolution spectroscopy is now being exploited with Ge detectors, which allows to measure Doppler broadenings and line shape details of these cosmic gamma-ray lines. Current results include an all-sky map and line shape measurement of positron annihilation emission, 26Al emission from the inner Galaxy and from the Cygnus region, a detection of 60Fe gamma-rays, and limits on 44Tiemission from Cas A and other candidate young supernova remnants; 22Na from novae still has not been seen. In this paper we discuss the experimental methods for such cosmic gamma-ray spectroscopy, and the corresponding astrophysical implications.