I will introduce the Killing-Yano tensor as a hidden symmetry responsible
for the "miraculous" properties of the four-dimensional Kerr black hole
spacetime. Recently, various motivations stimulated a renewed interest in
the exact solutions of higher-dimensional gravity. Of particular interest
are the higher-dimensional black hole spacetimes, the generalizations of
the Kerr geometry. I will demonstrate that despite their complexity they
still possess the Killing-Yano tensor. As an immediate consequence the
geodesic motion around these black holes is completely integrable and the
Hamilton-Jacobi and Klein-Gordon equations admit the separation of
variables.