  Modern astrophysical methods of determination of spins of rotating
stellar-mass black hole in close binaries and of supermassive black holes in
active galactic nuclei are briefly discussed. Effective spins of coalescing
binary black holes derived from LIGO/Virgo gravitational wave observations are
specially addressed. We consider three types of coalescing binaries: double
black holes, black hole-neutron star binaries and primordial double black
holes. The effective spins of coalescing astrophysical binary black holes and
black holes with neutron stars are calculated for two plausible models of black
hole formations from stellar core collapses (without or with additional
fallback from the stellar envelope) taking into account the stellar metallicity
and star formation rate evolution in the Universe. The calculated distributions
do not contradict the reported LIGO/Virgo observations. The effective spins of
primordial coalescing stellar-mass black holes can reach a few per cent due to
accretion spin-up in the cold external medium.
