  A typical galaxy is thought to contain tens of millions of stellar-mass black
holes, the collapsed remnants of once massive stars, and a single nuclear
supermassive black hole. Both classes of black holes accrete gas from their
environments. The accreting gas forms a flattened orbiting structure known as
an accretion disk. During the past several years, it has become possible to
obtain measurements of the spins of the two classes of black holes by modeling
the X-ray emission from their accretion disks. Two methods are employed, both
of which depend upon identifying the inner radius of the accretion disk with
the innermost stable circular orbit (ISCO), whose radius depends only on the
mass and spin of the black hole. In the Fe K method, which applies to both
classes of black holes, one models the profile of the
relativistically-broadened iron line with a special focus on the
gravitationally redshifted red wing of the line. In the continuum-fitting
method, which has so far only been applied to stellar-mass black holes, one
models the thermal X-ray continuum spectrum of the accretion disk. We discuss
both methods, with a strong emphasis on the continuum-fitting method and its
application to stellar-mass black holes. Spin results for eight stellar-mass
black holes are summarized. These data are used to argue that the high spins of
at least some of these black holes are natal, and that the presence or absence
of relativistic jets in accreting black holes is not entirely determined by the
spin of the black hole.
