This review summarises what we have learnt in the last two decades based on HI21 cm absorption observations about the cold interstellar medium (ISM) in the central regions of active galaxies and about the interplay between this gas and the active nucleus (AGN). HI absorption is a powerful tracer on all scales, from the parsec-scales close to the central black hole to structures of many tens of kpc tracing interactions and mergers of galaxies. Given the strong radio continuum emission often associated with the central activity, HI absorption observations can be used to study the HI near an active nucleus out to much higher redshifts than is possible using HI emission. In this way, HI absorption has been used to characterise in detail the gen...