Ultra-Light Dark Matter
  Ultra-light dark matter (ULDM) is a class of dark matter models (DM) where DM
is composed by bosons with masses ranging from $10^{-24}\, \mathrm{eV} < m <
\mathrm{eV}$. These models have been receiving a lot of attention in the past
few years given their interesting property of forming a Bose-Einstein
condensate (BEC) or a superfluid on galactic scales. BEC and superfluidity are
one of the most striking quantum mechanical phenomena manifest on macroscopic
scales, and upon condensation, the particles behave as a single coherent state,
described by the wavefunction of the condensate. The idea is that condensation
takes place inside galaxies while outside DM behaves like a normal cold
particle DM. This wave nature of DM on galactic scales that arise upon
condensation can address some of the curiosities of the behaviour of DM on
small scales while maintaining the successes of LCDM on large scales. There are
many models in the literature that describe a DM component that condenses in
galaxies. In this review, we are going to describe those models and classify
them according to the different ways they achieve condensation. For that, we
review the phenomena of BEC and superfluidity, and apply this knowledge to the
DM in order to explain their construction and phenomenology. We describe the
small scale challenges these models aim to solve and how ULDM alleviates them.
These models present a rich phenomenology that is manifest in different
astrophysical consequences. We review here the astrophysical and cosmological
tests used to constrain those models, together with new and future observations
that promise to test these models in different regimes. We finalize by showing
some predictions that are a consequence of the wave nature of this component,
like vortices and interference, that could represent a smoking gun in the
search of these rich and interesting alternative class of DM. (Abridged)
