Dark Matter Candidates of a Very Low Mass

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.