There is increasing evidence that the majority of dark matter is non-baryonic. Principal candidates are weakly interacting massive particles (WIMPS), axions, and neutrinos. There has been increasing effort on sensitive WIMP searches, motivated in particular by supersymmetry theory, which predicts a stable neutral particle in the mass range 10-1000 GeV. Interactions of these with normal matter would produce low energy nuclear recoils which could be observed by underground detectors capable of discriminating these from background. Current experimental progress is summarised, together with plans for more sensitive experiments. These include gaseous detectors with directional sensitivity, offering the prospect of a ‘dark matter telescope’ which would provide information on the dark matter velocity distribution. Axions could be detected by conversion to microwave photons, and experimental sensitivity is approaching the theoretically-required levels. Relic neutrinos could also form a component of the dark matter if any has a cosmologically significant mass, and the latter could be checked with a new detector able to detect the higher neutrino flavours from a Galactic supernova burst. More distant future possibilities are outlined for direct detection of relic neutrinos by coherent scattering.