  The nature of dark matter (DM) is one of the most relevant questions in
modern astrophysics. We present a brief overview of recent results that inquire
into a possible fermionic quantum nature of the DM particles, focusing mainly
on the interconnection between the microphysics of the neutral fermions and the
macrophysical structure of galactic halos, including their formation both in
the linear and non-linear cosmological regimes. We discuss the general
relativistic Ruffini-Arg\"uelles-Rueda (RAR) model of fermionic DM in galaxies,
its applications to the Milky Way, the possibility that the Galactic center
harbors a DM core instead of a supermassive black hole (SMBH), the S-cluster
stellar orbits with an in-depth analysis of the S2's orbit including
precession, the application of the RAR model to other galaxy types (dwarf,
elliptic, big elliptic and galaxy clusters), and universal galaxy relations.
All the above focusing on the model parameters constraints, most relevant to
the fermion mass. We also connect the RAR model fermions with particle physics
DM candidates, self-interactions, and galactic observables constraints. The
formation and stability of core-halo galactic structures predicted by the RAR
model and their relation to warm DM cosmologies are also treated. Finally, we
briefly discuss how gravitational lensing, dynamical friction, and the
formation of SMBHs can also probe the DM nature.
