From noncommutative space-time to quantum relativistic symmetries with fundamental mass parameter

We consider the simplest class of Lie-algebraic deformations of space-time algebra, with the selection of $\kappa$-deformations as providing quantum deformation of relativistic framework. We recall that the $\kappa$-deformation along any direction in Minkowski space can be obtained. Some problems of the formalism of $\kappa$-deformations will be considered. We shall comment on the conformal extension of light-like $\kappa$-deformation as well as on the applications to astrophysical problems.