This review summarises what we have learnt in the last two decades based on HI 21-cm absorption observations about the cold interstellar medium (ISM) in the central regions of active galaxies and the interplay between this gas and the active nucleus (AGN). HI absorption is a powerful tracer on all scales, from the pc scales to many tens of kpc. Given the strong radio continuum often associated with the central activity, HI absorption can be used to study the HI near an AGN out to much higher redshifts than is possible using HI emission. HI absorption has been used to characterise the general ISM in active galaxies, to trace the fuelling of radio-loud AGN, to study the feedback between the energy released by the AGN and the ISM, and the impact of such interactions on the evolution of galaxies and their AGN. In the last two decades, significant progress has been made in all these areas. It is now well established that many radio loud AGN are surrounded by small, regularly rotating gas disks that contain a significant fraction of HI. The structure of these disks has been traced down to parsec scales by VLBI observations. Young and recently restarted radio galaxies appear to have a high detection rate of HI. This is interesting in connection with the evolution of these AGN. This is confirmed by the discovery of fast, AGN-driven outflows of cold gas which give a direct view of the impact of the energy released by AGN. In addition, evidence has been collected that clouds of cold gas can play a role in fuelling the nuclear activity. This review ends by briefly describing the upcoming large, blind HI absorption surveys planned for the new radio telescopes which will soon become operational. These surveys will allow to significantly expand existing work, but will also allow to explore new topics, in particular the evolution of the cold ISM in AGN.
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