The cosmic microwave background and the cosmic expansion can be interpreted as evidence that the Universe underwent an extremely hot and dense phase about 14 Gyr ago. The nucleosynthesis computations tell us that the Universe emerged from this state with a very simple chemical composition: H, 2H, 3He, 4He, and traces of 7Li. All other nuclei where synthesised at later times. Our stellar evolution models tell us that, if a low-mass star with this composition had been created (a “zero-metal” star) at that time, it would still be shining on the Main Sequence today. Over the last 40 years there have been many efforts to detect such primordial stars but none has so-far been found. The lowest metallicity stars known have a metal content, Z, which is of the order of 10−4Z⊙. These are also the lowest metallicity objects known in the Universe. This seems to support the theories of star formation which predict that only high mass stars could form with a primordial composition and require a minimum metallicity to allow the formation of low-mass stars. Yet, since absence of evidence is not evidence of absence, we cannot exclude the existence of such low-mass zero-metal stars, at present. If we have not found the first Galactic stars, as a by product of our searches we have found their direct descendants, stars of extremely low metallicity (Z ≤ 10−3Z⊙). The chemical composition of such stars contains indirect information on the nature of the stars responsible for the nucleosynthesis of the metals. Such a fossil record allows us a glimpse of the Galaxy at a look-back time equivalent to redshift z = 10, or larger. The last ten years have been full of exciting discoveries in this field, which I will try to review in this contribution.