The   following   topics  will  be  briefly
discussed:
    Twist   realizations   of   kappa-Minkowski
spacetime as a deformed Hopf module algebras.
    Deformed  realizations  of the Poincare Lie
algebra,  its  kappa-Minkowski extension and de
Sitter Lie algebra
    Deformed dispersion relations corresponding
to   different  twists  parameters  and  doubly
special relativity theories
    Twisted  and q-deformations of the Poincare
Lie algebra in a classical basis

    The  talk is based on recent papers with A.
Pachol   (PRD79:   045012   -   arXiv:0812.0576
[math-ph] and arXiv:0903.5251 [hep-th]