Killing tensors have been thought of as describing
hidden symmetry of space(-time) since they are in
one-to-one correspondence with polynomial first
integrals of the geodesic equations. Then it has
been desirable to establish a method for finding
Killing tensors for a given space(-time). In this
talk, I would like to talk about how one should
search for Killing tensors for a given space(-time),
and, if requested, I would like to explain the
details of the derivation of several formulas used
in the method. Finally, I would like to discuss a
little the role of Killing tensors in the integration
of the Jacobi equations.