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Understanding superconductivity in its myriad forms arising in numerous different crystal architectures is one of the major quests of modern condensed matter physics. One promising avenue to gain local information about novel superconductors is the use of local probes to measure properties inside the unit cell. The application of muon spin spectroscopy to the study of various superconducting materials is reviewed. These experiments can be carried out as a function of temperature, magnetic field, and pressure and even in thin-film samples. They provide information about proximal magnetic phases and the nature of the superconducting state, as well as giving intriguing evidence of time-reversal symmetry breaking. To properly interpret the experimental results, it is necessary to have reliable information about the site of the implanted muon, as well as its stability. This can now be provided using density functional theory techniques.
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