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General Relativity is able to describe the dynamics of galaxies and largercosmic structures only if most of the matter in the Universe is dark, namely itdoes not emit any electromagnetic radiation. Intriguingly, on the scale ofgalaxies, there is strong observational evidence that the presence of darkmatter appears to be necessary only when the gravitational field inferred fromthe distribution of the luminous matter falls below an acceleration of theorder of 10^(-10) m/s^2. In the standard model, which combines Newtoniangravity with dark matter, the origin of this acceleration scale is challengingand remains unsolved. On the contrary, the full set of observations can beneatly described, and were partly predicted, by a modification of Newtoniandynamics, dubbed MOND, that does not resort to the existence of dark matter. Onthe scale of galaxy clusters and beyond, however, MOND is not as successful ason the scale of galaxies, and the existence of some dark matter appearsunavoidable. A model combining MOND with hot dark matter made of sterileneutrinos seems to be able to describe most of the astrophysical phenomenology,from the power spectrum of the cosmic microwave background anisotropies to thedynamics of dwarf galaxies. Whether there exists a yet unknown covariant theorythat contains General Relativity and Newtonian gravity in the weak field limit,and MOND as the ultra-weak field limit is still an open question.

The Acceleration Scale, Modified Newtonian Dynamics, and Sterile Neutrinos