Spins of black holes in coalescing compact binaries

Modern astrophysical methods for determining spins of rotating stellar-mass black holes 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. The effective spins of coalescing astrophysical binary black holes and black holes with neutron stars are calculated for two plausible models of black hole formation from stellar core collapses (without or with an additional fallback from the stellar envelope) taking the stellar metallicity and star formation rate evolution in the Universe into account. The calculated distributions are consistent with the reported LIGO/Virgo observations. Distributions of the effective spins expected in yet undiscovered neutron star - black hole binaries have been calculated. The effective spins of primordial coalescing stellar-mass black holes can reach a few percent due to the accretion spin-up in a cold external medium.