We discuss the details of the mass discrepancy phenomenon in galaxies
usually accounted by postulating the presence of a non luminous
component. In the theoretical framework of Newtonian gravity and Dark
matter halos we start by recalling the properties of the latter as
emerging from the state-of-the-art of numerical simulations performed
in the current LCDM scenario of cosmological structure formation. We
then report the complex and much-telling phenomenology of the
distribution of dark matter in spirals, ellipticals, and dwarf
spheroidals. Care will be given to show that such a coherent
observational framework is obtained from different and large samples
of galaxies and by means of very different methods of investigation
and by exploiting different tracers of the gravitational field. These
include rotation curve and dispersion velocities mass fitting, X-ray
gas property analysis, weak and strong lens signal mass decomposition,
analysis of halo and baryonic mass functions. We will then highlight
the impressive evidence that the distribution of dark and luminous
matter are closely correlated. Hints on how the empirical scenario of
the mass distribution in galaxies, including the Milky Way and the
nearby ones affects the cosmological investigations are given
throughout the talk. Among them, the theoretical constraints on the
elusive nature of the dark matter particles and its direct and
indirect searches. Finally, it is suggested that at least part of this
phenomenology should enter in the standard knowledge background of
cosmologists.