The standard model of cosmology — the “Lambda cold dark matter” model — is based on the idea that the dark matter is a collisionless elementary particle, probably a supersymmetric particle. This model (which mostly dates back to the 1980s) has been famously verified by observations of the cosmic microwave background radiation and the large-scale distribution of galaxies. However, the model has yet to be tested conclusively on the small scales appropriate to most astronomical objects, such as galaxies and clusters. I will review our current understanding of the distribution of dark matter on small scales which derives largely from large cosmological N-body simulations and I will discuss prospects for detecting dark matter, either through its gravitational effect on galaxies and clusters or, more directly, through gamma-ray annihilation radiation.