  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*10^7Msun),
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 disk. 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.
