Hierarchical mergers of stellar-mass black holes and their
  gravitational-wave signatures
  We review theoretical findings, astrophysical modeling, and current
gravitational-wave evidence of hierarchical stellar-mass black-hole mergers.
While most of the compact binary mergers detected by LIGO and Virgo are
expected to consist of first-generation black holes formed from the collapse of
stars, others might instead be of second (or higher) generation, containing the
remnants of previous black-hole mergers. Such a subpopulation of hierarchically
assembled black holes presents distinctive gravitational-wave signatures,
namely higher masses, possibly within the pair-instability mass gap, and
dimensionless spins clustered at the characteristic value of $\sim$0.7. In
order to produce hierarchical mergers, astrophysical environments need to
overcome the relativistic recoils imparted to black-hole merger remnants, a
condition which prefers hosts with escape speeds $\gtrsim$ 100 km/s. Promising
locations for efficient production of hierarchical mergers include nuclear star
clusters and accretion disks surrounding active galactic nuclei, though
environments that are less efficient at retaining merger products such as
globular clusters may still contribute significantly to the detectable
population of repeated mergers. While GW190521 is the single most promising
hierarchical-merger candidate to date, constraints coming from large population
analyses are becoming increasingly more powerful.
