  We review dark matter (DM) candidates of a very low mass, appearing in the
window below the traditional weakly-interacting massive particle $m_\chi
\lesssim 10$ GeV and extending down to $m_\chi \gtrsim 1$ meV, somewhat below
the mass limit where DM becomes wavelike. Such candidates are motivated by
hidden sectors such as Hidden Valleys, which feature hidden forces and rich
dynamics, but have evaded traditional collider searches looking for New Physics
because of their relatively weak coupling to the Standard Model. Such sectors
can still be detected through dedicated low-energy colliders which, through
their intense beams, can have sensitivity to smaller couplings, or through
astrophysical observations of the evolution of DM halos and stellar structures
which, through the Universe's epochs, can be sensitive to small DM
interactions. We also consider mechanisms where the DM abundance is fixed
through the interaction with the SM, which directly motivates the search for
light DM in terrestrial experiments. The bulk of this review is dedicated to
the new ideas that have been proposed for directly detecting such DM candidates
of a low mass, through nuclear recoils, electronic excitations, or collective
modes such as phonons and magnons. The rich tapestry of materials and modes in
the Condensed Matter landscape is reviewed, along with specific prospects for
detection.
