  Intermediate-mass black holes (IMBHs), with masses in the range $100-10^{6}$
M$_{\odot}$, are the link between stellar-mass BHs and supermassive BHs
(SMBHs). They are thought to be the seeds from which SMBHs grow, which would
explain the existence of quasars with BH masses of up to 10$^{10}$ M$_{\odot}$
when the Universe was only 0.8 Gyr old. The detection and study of IMBHs has
thus strong implications for understanding how SMBHs form and grow, which is
ultimately linked to galaxy formation and growth, as well as for studies of the
universality of BH accretion or the epoch of reionisation. Proving the
existence of seed BHs in the early Universe is not yet feasible with the
current instrumentation; however, those seeds that did not grow into SMBHs can
be found as IMBHs in the nearby Universe. In this review I summarize the
different scenarios proposed for the formation of IMBHs and gather all the
observational evidence for the few hundreds of nearby IMBH candidates found in
dwarf galaxies, globular clusters, and ultraluminous X-ray sources, as well as
the possible discovery of a few seed BHs at high redshift. I discuss some of
their properties, such as X-ray weakness and location in the BH mass scaling
relations, and the possibility to discover IMBHs through high velocity clouds,
tidal disruption events, gravitational waves, or accretion disks in active
galactic nuclei. I finalize with the prospects for the detection of IMBHs with
up-coming observatories.
