Abstract

We have had the chance to live through a fascinating revolution in measuring the fundamental empirical cosmological Hubble law. The key progress is analysed: improvement of observational means ; understanding of the biases that affect both distant and local determinations of the Hubble constant; new theoretical and observational results. These circumstances encourage us to take a critical look at some facts and ideas related to the cosmological red-shift. This is important because we are probably on the eve of a new understanding of our Universe, heralded by the need to interpret some cosmological key observations in terms of unknown processes and substances.