Dark matters on the scale of galaxies.

The cold dark matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark matter model faces persistent challenges on the scales of galaxies. {Indeed,} N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed} within the cold dark matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. { We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and $f(R)$ gravity.