  We review the application of twist deformation formalism and the construction
of noncommutative gauge theory on $\kappa$-Minkowski space-time. We compare two
different types of twists: the Abelian and the Jordanian one. In each case we
provide the twisted differential calculus and consider ${U}(1)$ gauge theory.
Different methods of obtaining a&nbsp;gauge invariant action and related
problems are thoroughly discussed.
