We know that dark matter constitutes 85 per cent of all the matter in the Universe, but we do not know of what it is made. After a brief introduction on dark matter candidates, I will focus on WIMPs (weakly interacting massive particles), which occupy a special place since they arise naturally from new theories that seek to extend the standard model of particle physics. I will review the prospects for discovering WIMPs at the Large Hadron Collider at CERN and with the upcoming generation of astroparticle experiments, and emphasize the complementarity of different detection strategies.