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We discuss constraints on black hole spin and spin-related astrophysics as derived from X-ray spectroscopy. After a brief discussion about the robustness with which X-ray spectroscopy can be used to probe strong gravity, we summarize how these techniques can constrain black hole spin. In particular, we highlight XMM-Newton studies of the Seyfert galaxy MCG-6-30-15 and the stellar-mass black hole GX 339-4. The broad X-ray iron line profile, together with reasonable and general astrophysical assumptions, allow a non-rotating black hole to be rejected in both of these sources. If we make the stronger assertion of no emission from within the innermost stable circular orbit, the MCG-6-30-15 data constrain the dimensionless spin parameter to be a > 0.93. Furthermore, these XMM-Newton data are already providing evidence for exotic spin-related astrophysics in the central regions of this object. We …