Properties of (skew-symmetric) conformal Yano-Killing tensors are
reviewed. The examples of CYK tensors in Minkowski, Kerr, de Sitter and
anti-de Sitter spacetimes are discussed. Basic facts and definitions of
the spin-2 field and conformal Yano-Killing tensors are
introduced. Application of those two objects provides a precise
definition of quasi-local gravitational charge. It leads to geometric
definition of the asymptotic flat spacetime: `strong asymptotic
flatness', which guarantees well defined total angular momentum. Conformal
rescaling of conformal Yano-Killing tensors and relations between Yano
and CYK tensors are discussed. Pullback of these objects to a submanifold
is used to construct all solutions of a CYK equation in anti-de Sitter
and de Sitter spacetimes. Properties of asymptotic conformal Yano-Killing
tensors are examined for asymptotic anti-de Sitter spacetimes. Explicit
asymptotic forms of them are derived. The results are used to construct
asymptotic chargesin asymptotic AdS spacetime. Well known examples like
Schwarzschild-AdS, Kerr-AdS and NUT-AdS are examined carefully in the
construction of the concept of energy, angular momentum and dual mass in
asymptotic AdS spacetime. Other applications: symmetric Killing tensors
and constants of motion along geodesics.