  General relativity and its Newtonian weak field limit are not sufficient to
explain the observed phenomenology in the Universe, from the formation of
large-scale structures to the dynamics of galaxies, with the only presence of
baryonic matter. The most investigated cosmological model, the $\Lambda$CDM,
accounts for the majority of observations by introducing two dark components,
dark energy and dark matter, which represent $\sim$95% of the mass-energy
budget of the Universe. Nevertheless, the $\Lambda$CDM model faces important
challenges on the scale of galaxies. For example, some very tight relations
between the properties of dark and baryonic matters in disk galaxies, such as
the baryonic Tully-Fisher relation (BTFR), the mass discrepancy-acceleration
relation (MDAR), and the radial acceleration relation (RAR), which see the
emergence of the acceleration scale $a_0 \simeq 1.2 \times 10^{-10}$ m
s$^{-2}$, cannot be intuitively explained by the CDM paradigm, where cosmic
structures form through a stochastic merging process. An even more outstanding
coincidence is due to the fact that the acceleration scale $a_0$, emerging from
galaxy dynamics, also seems to be related to the cosmological constant
$\Lambda$. Another challenge is provided by dwarf galaxies, which are darker
than what is expected in their innermost regions. These pieces of evidence can
be more naturally explained, or sometimes even predicted, by modified theories
of gravity, that do not introduce any dark fluid. I illustrate possible
solutions to these problems with the modified theory of gravity MOND, which
departs from Newtonian gravity for accelerations smaller than $a_0$, and with
Refracted Gravity, a novel classical theory of gravity introduced in 2016,
where the modification of the law of gravity is instead regulated by a density
scale.
