Since all heavy chemical elements are supposed to be made in stars one would expect that low-mass (slowly evolving) stars from the first stellar generation, with no heavy elements at all in their surface layers, should be possible to find. Such a generation could have had very great significance for the formation and early evolution of galaxies. For 35 years searches for remaining such stars have been conducted, with negative results. In the last five years, however, indirect evidence for a very early stellar generation, preceding the formation of galaxies, has been traced in the Cosmic Microwave Background. Theoretically, such stars may be expected to evolve in ways remarkably different from those of normal stars. A few stars with very low abundances of heavy elements, and quite odd elemental composition, have also been found. What do they tell us about the first stellar generation?