  Some classes of Deformed Special Relativity (DSR) theories are reconsidered
within the Hopf algebraic formulation. For this purpose we shall explore a
minimal framework of deformed Weyl-Heisenberg algebras provided by a smash
product construction of DSR algebra. It is proved that this DSR algebra, which
uniquely unifies $\kappa$-Minkowski spacetime coordinates with Poincar\'e
generators, can be obtained by nonlinear change of generators from undeformed
one. Its various realizations in terms of the standard (undeformed)
Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of
DSR theories in terms of relativistic (St\"uckelberg version) Quantum
Mechanics. On this basis we review some recent results concerning twist
realization of $\kappa$-Minkowski spacetime described as a quantum covariant
algebra determining a deformation quantization of the corresponding linear
Poisson structure. Formal and conceptual issues concerning quantum
$\kappa$-Poincar\'e and $\kappa$-Minkowski algebras as well as DSR theories are
discussed. Particularly, the so-called "$q$-analog" version of DSR algebra is
introduced. Is deformed special relativity quantization of doubly special
relativity remains an open question. Finally, possible physical applications of
DSR algebra to description of some aspects of Planck scale physics are shortly
recalled.
