More than 80 years after its first postulation in modern form, the existence and distribution of dark matter in our Universe is well established. Dark matter is the gravitational glue that holds together galaxies, galaxy clusters and structures on the largest cosmological scales, and an essential component to explain the observed fluctuations in the cosmic microwave background. Yet its existence is inferred indirectly, through its gravitational influence on luminous matter, and its nature is not known. A viable hypothesis is that dark matter is made of new, elementary particles, with allowed masses and interaction strengths spanning a wide range. Two well-motivated classes of candidates are axions and weakly interacting massive particles (WIMPs), and experimental efforts have now reached sensitivities that allow them to test this hypothesis. Axions, produced non-thermally in the early Universe, can be detected by exploiting their predicted couplings to photons and electrons. WIMPs can be detected directly by looking for their collisions with atomic nuclei ultra-low background detectors, or indirectly, through the observation of their annihilation products such as neutrinos, gamma rays, positrons and antiprotons over the astrophysical background. A complementary method is the production of dark matter particles at colliders such as the Large Hadron Collider, where they could be observed indirectly via missing transverse energy, or via associated particle production. I will review the main experimental efforts to search for dark matter particles, and the existing constraints on the interaction cross sections. I will also discuss future experiments, their complementarity and their ability to measure the properties of these particles.