  In this paper, we discuss hidden symmetries in rotating black hole
spacetimes. We start with an extended introduction which mainly summarizes
results on hidden symmetries in four dimensions and introduces Killing and
Killing-Yano tensors, objects responsible for hidden symmetries. We also
demonstrate how starting with a principal CKY tensor (that is a closed
non-degenerate conformal Killing-Yano 2-form) in 4D flat spacetime one can
"generate" 4D Kerr-NUT-(A)dS solution and its hidden symmetries. After this we
consider higher-dimensional Kerr-NUT-(A)dS metrics and demonstrate that they
possess a principal CKY tensor which allows one to generate the whole tower of
Killing-Yano and Killing tensors. These symmetries imply complete integrability
of geodesic equations and complete separation of variables for the
Hamilton-Jacobi, Klein-Gordon, and Dirac equations in the general
Kerr-NUT-(A)dS metrics.
