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Many theoretically well-motivated extensions of the Standard Model of particle physics predict the existence of very weakly interacting ultralight particles, such as the axion and similar Nambu-Goldstone bosons. They may constitute the mysterious dark matter in the Universe and solve some puzzles in stellar and high-energy astrophysics. There are new, relatively small experiments around the globe, which started to hunt for these elusive particles and complement the search for physics beyond the Standard Model at the Large Hadron Collider.