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The Hubble law discovered in 1929, i.e. the linear relation between the recession velocity of galaxies and their distance, is the cornerstone of modern cosmology and of the Big Bang model. In this model, the proportionality constant H0 in this relation, the so-called Hubble constant, is also the ratio of the expansion rate and size scale of the cosmos, the inverse ratio thus directly giving the age (and characteristic length) scale of the cosmos. To accurately determine H0 has thus been a major focus in observational cosmology and astrophysics over the past 90 years. However, the history of determining H0 has been full of systematic problems, inconsistencies and controversies from its very beginnings. The late 1990s saw a convergence of results, a consolidation of H0 around 72 km/sec/Mpc (with an accuracy better than 10%) and, thanks to supernovae as standard candles, the surprising result that the expansion of the universe is not slowing down under its own gravity, but rather accelerating. Recent years have, however, seen a re-emergence of an inconsistency between the value of H0 inferred from the scales set by the universe at early epochs and the value derived from the local distance scale. The ESA mission Planck has further tightened the first value, now corresponding to 67.5±0.5 km/sec/Mpc, while a reanalysis of the local distance scale gives raise to 73.5±1.6 km/sec/Mpc, these measurements thus being inconsistent at the 3.5σ level. Should this discrepancy eventually turn out to be clearly significant, its implication would be ground breaking – it would imply that either the early universe physics is less well understood than we thought, or there is a significant discrepancy in our local distance scale (which implies issues with our understanding of stellar structure), or it would be the first significant hint that the accelerated expansion cannot be explained with the simplest cosmological model, one with a cosmological constant, but rather requires a more dynamic dark energy. The next few years are likely to be particularly interesting for further study of this discrepancy. Ground based CMB experiments in the high Andes and at the South Pole, the ESA cornerstone mission Gaia and other methods to measure H0 are expected to provide results with increasing accuracy. It is thus the perfect time now to bring together the experts in the various field of astronomy and astrophysics that are concerned with the determination of H0 and the implications of these results, and to discuss the most recent results, prospects, and possible implications, and provide them to a broader audience of physicists.