  A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e)
algebra (QPA) is developed. We show that the representations of this algebra
are closely connected with the representations of the non-deformed Poincar\'e
algebra. A theory of tensor operators for QPA is considered in detail.
Necessary and sufficient conditions are found in order for scalars to be
invariants. Covariant components of the four-momenta and the Pauli-Lubanski
vector are explicitly constructed.These results are used for the construction
of some q-relativistic equations. The Wigner-Eckart theorem for QPA is proven.
