  We present a short review describing the use of noncommutative space-time in
quantum-deformed dynamical theories: classical and quantum mechanics as well as
classical and quantum field theory. We expose the role of Hopf algebras and
their realizations (noncommutative modules) as important mathematical tool
describing quantum-deformed symmetries: quantum Lie groups and quantum Lie
algebras. We consider in some detail the most studied examples of
noncommutative space-time geometry: the canonical and $\kappa$-deformed cases.
Finally we briefly describe the modifications of Einstein gravity obtained by
introduction of noncommutative space-time coordinates.
