The standard model of accretion onto black holes (BHs) predicts formation of an optically-thick accretion disc extending down to the innermost stable circular orbit (ISCO), which explains well the soft state of BH binaries. However, this model cannot explain states in which BH binaries and AGNs predominantly emit hard X-rays. It has to be instead emitted by some hot plasma. The location of this plasma has been the subject of an intense controversy. According to one view, the disc evaporates and changes to a hot flow relatively far from the BH. According to the other, the disc still extends down to the ISCO, and the hot plasma is located very close to both its inner edge and the horizon. The former scenario explains a large number of observations. Arguments for the latter are given mainly by observations of broad Fe K emission lines due to reflection on the disc, lines whose broadening is explained by extreme relativistic effects and therefore must originate very close to the BH. We propose an International Team that will discuss the arguments of both sides, summarise the current status of this issue, and devise projects that could lead to a definitive resolution of this controversy.