Killing-Yano symmetry is a fundamental symmetry which plays a crucial role in higher-dimensional rotating black hole spacetimes with spherical horizon topology, in the case that the supporting matter consists of a cosmological constant alone. Such black holes are uniquely characterised by the existence of this symmetry and derive from it many remarkable properties, such as complete integrability of geodesic motion, separability of the scalar, Dirac and gravitational perturbations and the special algebraic type of the Weyl tensor. Unfortunately, black holes of more general theories with additional matter content, such as the black holes of various supergravities or string theories, are usually much more complicated and the presence of matter tends to spoil many of the elegant characteristics of their vacuum brethren. On the other hand, it is known that for at least some of thease balck holes one can define an appropriate generalisation of the Killing-Yano symmetry and infer some of the black hole properties from it. In this talk, we begin with making a historical review of hidden symmetry of vacuum rotating black holes and generalise it to supergravity black holes. We will also see that one can constuct from the generalised Killing-Yano symmetry some new exact solutions of various supergravities, which generalise known balck hole solutions as well as Calabi-Yau and Sasakian manifolds.