Abstract. Fast variability studies of accreting black holes in the Galaxy offer us a unique opportunity to measure the spins of black holes and test the strong-field behavior of general relativity. In this review, I summarize the arguments often used in attempts of measuring the spins of black holes, concentrating on their theoretical foundations. I also argue that X-ray studies of accreting black holes will be able to provide in the future strong constraints on deviations from general relativity in the strong-field regime
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