  Constructing renormalizable models on non-commutative spaces constitutes a
big challenge. Only few examples of renormalizable theories are known, such as
the scalar Grosse-Wulkenhaar model. Gauge fields are even more difficult, since
new renormalization techniques are required which are compatible with the
inherently non-local setting on the one hand, and also allow to properly treat
the gauge symmetry on the other hand. In this proceeding (which is based on my
talk given at the ``Workshop on Noncommutative Field Theory and Gravity'' in
Corfu/Greece, September 8 -- 15, 2013), I focus on this last point and present
new extensions to existing renormalization schemes (which are known to work for
gauge field theories in commutative space) adapted to non-commutative Moyal
space.
