The goal of the proposed project is to search for and study several candidates for the dark matter. Recent data from the Planck mission show that our Universe contains 4.9% ordinary matter, 26.8% dark matter and 68.3% dark energy. One of the major efforts in particle physics today is to reveal the composition of the dark matter. Nowadays, it is known that neutrinos constitute only a tiny fraction of the dark matter, while the rest is made of yet unobserved particles theoretically predicted in various extensions of the Standard Model. Two leading dark-matter candidates are the Weakly Interacting Massive Particles (WIMPs), and the axion - a light pseudoscalar associated with the spontaneous breaking of U(1) Peccei-Quinn symmetry, a mechanism originally introduced to explain the absence of CP violation in strong interactions. This concept has been generalized to further axion-like particles (ALPs), which may arise as Nambu-Goldstone bosons from the breaking of various global symmetries. Possible dark matter candidates also include so-called WISPs, i.e., a variety of sub-eV (or slim) weakly-coupled particles such as hidden-sector photons and chameleons. A large number of theoretical ideas and hypotheses have been put forward to explain what the dark mater particles are, but only experimental data will be able to answer which, if any, of these ideas is correct. In the proposed project we are planning to continue and extend searches for axions, ALPs, and WISPs in experiments CAST (CERN Axion Solar Telescope) - currently the most sensitive axion helioscope in the world and its successor IAXO (International Axion Observatory). The discovery of such particles would be a ground-breaking result for particle physics since it would be a clean evidence of physics beyond Standard Model, but even in case of non-detection, CAST and IAXO will be able to exclude large parts of yet unexplored regions of the relevant parameter spaces for these particles.