  This article reviews the construction and some applications of twisted
Poincare-covariant quantum fields on the Moyal plane. The Drinfeld twist, which
plays a key mathematical role in this construction, is then applied to the case
of discrete groups, with a view to applications to geons in quantum gravity.
The Poincare-twisted fields can also be applied to study the CMB anisotropies,
and corrections to the power spectrum are used to put constraints on spacetime
noncommutativity. The article also addresses the issue of the difference
between Moyal and Voros quantum fields. Finally, it is pointed out that the
Euclidean functional integrals of QFTs on the Moyal plane do not, in general,
obey reflection positivity.
