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.
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