  At the time of defining the science objectives of the INTernational Gamma-Ray
Astrophysics Laboratory (INTEGRAL), such a rapid and spectacular development of
multi-messenger astronomy could not have been predicted, with new impulsive
phenomena becoming accessible through different channels.
  Neutrino telescopes have routinely detected energetic neutrino events coming
from unknown cosmic sources since 2013. Gravitational wave detectors opened a
novel window on the sky in 2015 with the detection of the merging of two black
holes and in 2017 with the merging of two neutron stars, followed by signals in
the full electromagnetic range. Finally, since 2007, radio telescopes detected
extremely intense and short burst of radio waves, known as Fast Radio Bursts
(FRBs) whose origin is for most cases extragalactic, but enigmatic.
  The exceptionally robust and versatile design of the INTEGRAL mission has
allowed researchers to exploit data collected not only with the pointed
instruments, but also with the active cosmic-ray shields of the main
instruments to detect impulses of gamma-rays in coincidence with unpredictable
phenomena. The full-sky coverage, mostly unocculted by the Earth, the large
effective area, the stable background, and the high duty cycle (85%) put
INTEGRAL in a privileged position to give a major contribution to
multi-messenger astronomy.
  In this review, we describe how INTEGRAL has provided upper limits on the
gamma-ray emission from black-hole binary mergers, detected a short gamma-ray
burst in coincidence with a binary neutron star merger, contributed to define
the spectral energy distribution of a blazar associated with a neutrino event,
set upper limits on impulsive and steady gamma-ray emission from cosmological
FRBs, and detected a magnetar flare associated with fast radio bursting
emission.
