This review summarises what we have learnt in the last two decades based on H I 21-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). H I 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, H I absorption observations can be used to study the H I near an active nucleus out to much higher redshifts than is possible by using H I emission. In this way, H I absorption has been used to characterise in detail the general ISM in active galaxies, to trace the fuelling of radio-loud AGN, to study the feedback occurring between the energy released by the active nucleus and the ISM, and the impact of such interactions on the evolution of galaxies and of 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 H I. The structure of these disks has been traced down to parsec scales by VLBI observations. Some groups of objects, and in particular young and recently restarted radio galaxies, appear to have a particularly high detection rate of H I. This is interesting in connection with the evolution of these AGN and their impact on the surrounding ISM. This is further confirmed by an important discovery, made thanks to technical upgrades of radio telescopes, namely the presence of fast, AGN-driven outflows of cold gas which give a direct view of the impact of the energy released by AGN on the evolution of galaxies (AGN feedback). 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 H I 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.