Several of the supposedly anhydrous major minerals of the upper mantle have been shown to regularly contain small amounts of hydrogen. The concentrations measured in the most important minerals obtained from mantle xenoliths are, expressed in ppm H2O, 100-1300 for clinopyroxene, 60-650 for orthopyroxene, 0- 140 for olivine and 1-200 for garnet. Hydrogen is normally structurally incorporated as hydroxyl ions, and in many cases the hydrogen ions seem to act as charge compensators associated with point defects, such as metal vacancies or substitution by mono- or trivalent cations. The determination of the exact amount of hydrogen stored in these nominally anhydrous upper mantle minerals is a key-step toward quantification of the water content of the mantle, as well as understanding of its internal water cycle. For instance, a concentration of 100 ppm H2O homogeneously distributed within the upper mantle above 410 km depth is approximately equivalent to a 100 m water layer at the Earth's surface. However, the relatively fast kinetics of dehydrogenation with concomitant oxidation of iron within these minerals, implies that hydrogen as well as Fe3+ concentrations in equilibrium with mantle conditions might be different from those measured from recovered xenolith samples. High-pressure experimental measurements of hydrogen solubility as a function of PH2O show a trend similar to the hydrogen contents of natural samples, with hydrogen saturation levels that decrease following the mineral series: diopside > enstatite > olivine > pyrope. Except pyrope, these minerals may incorporate more than 1000 ppm H2O. Based on recent data of water solubility, stability and partitioning, we suggest that an entire upper mantle saturated in hydrogen is highly unprobable and that the maximum average amount of hydrogen stored in the nominally anhydrous minerals of the upper mantle is around 600 ppm H2O. Despite the important progress achieved during the last years, our knowledge of the concentration of hydrogen stored as point defects in the mantle above 410 km is still too poorly constrained. The importance of nominally anhydrous minerals for the water budget of the upper mantle is now well established but still awaits complete quantification.