  Identifying the nature of dark matter (DM) has long been a pressing question
for particle physics. In the face of ever-more-powerful exclusions and null
results from large-exposure searches for TeV-scale DM interacting with nuclei,
a significant amount of attention has shifted to lighter (sub-GeV) DM
candidates. Direct detection of the light dark matter in our galaxy by
observing DM scattering off a target system requires new approaches compared to
prior searches. Lighter DM particles have less available kinetic energy, and
achieving a kinematic match between DM and the target mandates the proper
treatment of collective excitations in condensed matter systems, such as
charged quasiparticles or phonons. In this context, the condensed matter
physics of the target material is crucial, necessitating an interdisciplinary
approach. In this review, we provide a self-contained introduction to direct
detection of keV--GeV DM with condensed matter systems. We give a brief survey
of dark matter models and basics of condensed matter, while the bulk of the
review deals with the theoretical treatment of DM-nucleon and DM-electron
interactions. We also review recent experimental developments in detector
technology, and conclude with an outlook for the field of sub-GeV DM detection
over the next decade.
