Modified Newtonian Dynamics (MOND): Observational Phenomenology and
  Relativistic Extensions
  A wealth of astronomical data indicate the presence of mass discrepancies in
the Universe. The motions observed in a variety of classes of extragalactic
systems exceed what can be explained by the mass visible in stars and gas.
Either (i) there is a vast amount of unseen mass in some novel form - dark
matter - or (ii) the data indicate a breakdown of our understanding of dynamics
on the relevant scales, or (iii) both. Here, we first review a few outstanding
challenges for the dark matter interpretation of mass discrepancies in
galaxies, purely based on observations and independently of any alternative
theoretical framework. We then show that many of these puzzling observations
are predicted by one single relation - Milgrom's law - involving an
acceleration constant (or a characteristic surface density) of the order of the
square-root of the cosmological constant in natural units. This relation can at
present most easily be interpreted as the effect of a single universal force
law resulting from a modification of Newtonian dynamics (MOND) on galactic
scales. We exhaustively review the current observational successes and problems
of this alternative paradigm at all astrophysical scales, and summarize the
various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to
effectively embed this modification of Newtonian dynamics within a relativistic
theory of gravity.
