  We shall outline two ways of introducing the modification of Einstein's
relativistic symmetries of special relativity theory - the Poincar\'{e}
symmetries. The most complete way of introducing the modifications is via the
noncocommutative Hopf-algebraic structure describing quantum symmetries. Two
types of quantum relativistic symmetries are described, one with constant
commutator of quantum Minkowski space coordinates
($\theta_{\mu\nu}$-deformation) and second with Lie-algebraic structure of
quantum space-time, introducing so-called $\kappa$-deformation. The third
fundamental constant of Nature - fundamental mass $\kappa$ or length $\lambda$
- appears naturally in proposed quantum relativistic symmetry scheme. The
deformed Minkowski space is described as the representation space (Hopf-module)
of deformed Poincar\'{e} algebra. Some possible perspectives of
quantum-deformed relativistic symmetries will be outlined.
