  We study the Hardy identities and inequalities on Cartan-Hadamard manifolds
using the notion of a Bessel pair. These Hardy identities offer significantly
more information on the existence/nonexistence of the extremal functions of the
Hardy inequalities. These Hardy inequalities are in the spirit of
Brezis-V\'{a}zquez in the Euclidean spaces. As direct consequences, we
establish several Hardy type inequalities that provide substantial improvements
as well as simple understandings to many known Hardy inequalities and
Hardy-Poincar\'{e}-Sobolev type inequalities on hyperbolic spaces in the
literature.
