Intermediate-mass black holes (IMBHs) are a long-sought ‘missing link’ in black hole evolution. Only a few other IMBH candidates have been found to date. Most known black holes are either extremely massive, like the supermassive black holes that lie at the cores of large galaxies, or relatively lightweight, with a mass less than 100 times that of the Sun. Black holes are one of the most extreme environments humans are aware of, and so they are a testing ground for the laws of physics and our understanding of how the Universe works. If IMBHs exist, how common are they? Does a supermassive black hole grow from an IMBH? How do IMBHs themselves form? Are dense star clusters their favoured home?