Quantum groups and deformed special relativity

The structure and properties of possible q-Minkowski spaces are reviewed and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing the covariance properties of these algebras with respect to the corresponding q-deformed Lorentz groups as described by appropriate reflection equations. This allow us to give an unified treatment for different q-Minkowski algebras. Some isomorphisms among the space-time and derivative algebras are demonstrated, and their representations are described briefly. Finally, some. physical consequences and open problems are discussed.