The Cherenkov Telescope Array (CTA) is an international project for a next-generation ground-based gamma-ray observatory. CTA, conceived as an array of few tens of imaging atmospheric Cherenkov telescopes, is aiming to improve on the current generation sensitivity by an order of magnitude, with an energy coverage from a few tens of GeV to 100 TeV. CTA can potentially provide clues about major open questions in fundamental physics, such as the elusive nature of the dark matter component of the Universe. Here we study the CTA prospects for detection of dark matter, evaluating different possible array layouts, based on the expected performance of the instrument as obtained from Monte Carlo simulations. We consider different observation strategies and classes of targets: dwarf spheroidal galaxies of the Milky Way, the Galactic Center, and clusters of galaxies. We also explore the possible search for dark matter spatial signatures, as well as the search for axion-like particles as dark matter particle candidates.