The spin of supermassive black holes

Black hole spin is a quantity of great interest to both physicists and astrophysicists. We review the current status of spin measurements in supermassive black holes (SMBH). To date, every robust SMBH spin measurement uses x-ray reflection spectroscopy, so we focus almost exclusively on this technique as applied to moderately-luminous active galactic nuclei (AGN). After describing the foundations and uncertainties of the method, we summarize the current status of the field. At the time of writing, observations by XMM-Newton, Suzaku and NuSTAR have given robust spin constraints on 22 SMBHs. We find a significant number of rapidly rotating SMBHs (with dimensionless spin parameters a > 0.9) although, especially at the higher masses (M > 4 x 10(7)M(circle dot)), there are also some SMBHs with intermediate spin parameters. This may be giving us our first hint at a mass-dependent spin distribution which would, in turn, provide interesting constraints on models for SMBH growth. We also discuss the recent discovery of relativistic x-ray reverberation which we can use to 'echo map' the innermost regions of the accretion disc. The ultimate development of these reverberation techniques, when applied to data from future high-throughput x-ray observatories such as LOFT, ATHENA+, and AXSIO, will permit the measurement of black hole spin by a characterization of strong-field Shapiro delays. We conclude with a brief discussion of other electromagnetic methods that have been attempted or are being developed to constrain SMBH spin.