From the text: The author reviews recent research on quantum deformations of the Poincar\'e supergroup and superalgebra. It is based on a series of papers (coauthored by P. Kosi\'nski, J. Lukierski, P. Ma\'slanka and A. Nowicki) and is motivated by both mathematics and physics. On the mathematical side, some new examples of noncommutative and noncocommutative Hopf superalgebras have been discovered. Moreover, it turns out that they have an interesting internal structure of graded bicrossproduct. As far as physics is concerned, the discussed deformations are closely related to quantum deformations of the (not super!) Poincar\'e group and algebra, which has become a subject of considerable interest in recent years. These deformations involve dimensional parameter $\kappa$ (the classical case corresponds to the limit $\kappa \to \infty)$ and some authors tried to impose limits on possible numerical values of $\kappa$ coming from physical arguments.