The MOND phenomenology
  The Lambda-CDM cosmological model is succesful at reproducing various
independent sets of observations concerning the large-scale Universe. This
model is however currently, and actually in principle, unable to predict the
gravitational field of a galaxy from it observed baryons alone. Indeed the
gravitational field should depend on the relative contribution of the particle
dark matter distribution to the baryonic one, itself depending on the
individual assembly history and environment of the galaxy, including a lot of
complex feedback mechanisms. However, for the last thirty years, Milgrom's
formula, at the heart of the MOND paradigm, has been consistently succesful at
predicting rotation curves from baryons alone, and has been resilient to all
sorts of observational tests on galaxy scales. We show that the few individual
galaxy rotation curves that have been claimed to be highly problematic for the
predictions of Milgrom's formula, such as Holmberg II or NGC 3109, are actually
false alarms. We argue that the fact that it is actually possible to predict
the gravitational field of galaxies from baryons alone presents a challenge to
the current Lambda-CDM model, and may indicate a breakdown of our understanding
of gravitation and dynamics, and/or that the actual lagrangian of the dark
sector is very different and richer than currently assumed. On the other hand,
it is obvious that any alternative must also, in fine, reproduce the successes
of the Lambda-CDM model on large scales, where this model is so well-tested
that it presents by itself a challenge to any such alternative.
