  This paper contains a brief review of the remarkable properties of higher
dimensional rotating black holes with the spherical topology of the horizon. We
demonstrate that these properties are connected with and generated by a special
geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The
most general solution, describing such black holes, Kerr-NUT-ADS metric, admits
this structure. Moreover a solution of the Einstein Equations with (or without)
a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This
object (PCKYT) is responsible for such remarkable properties of higher
dimensional rotating black holes as: (i) complete integrability of geodesic
equations and (ii) complete separation of variables of the important field
equations.
