The Big Bang created primordial material from which the first stars formed. These stars exploded as supernovae and polluted the material from which subsequent generations of stars were made. Astronomers have had difficulty in finding stars made of the pure Big Bang material, but they have found stars with very little polluting material. The age of these cosmological relics of the first eras sets a lower limit for the age of the Universe we live in. European astronomers and their colleagues worldwide have joined in the effort to discover and date these, the oldest stars, and cast a glance into the obscure phases between the very first seconds of the existence of the Universe and the epoch at which galaxies and clusters of stars matured. Many independent techniques have been devised to date the oldest stars and stellar systems in the Universe. Some of them are briefly reviewed. The age of the oldest stars is now converging on a value in the range from 12 to 15 thousand million years. However, a large uncertainty still exists and a value as a large as 17 to18 thousand million years cannot be totally ruled out. Such a large value would be difficult to reconcile with the age of the Universe based on cosmological data. Significant improvements in the uncertainties of this situation are expected from the 8–1 m telescopes and space missions of the next decade.