  We have had the chance to live through a fascinating revolution in measuring
the fundamental empirical cosmological Hubble law. The key progress is analysed
: 1) improvement of observational means (ground-based radio and optical
observations, space missions) ; 2) understanding of the biases that affect both
distant and local determinations of the Hubble constant; 3) 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.
