  This is the written version of a talk I gave at the 35th Symposium Ahrenshoop
in Berlin, Germany, August 2002. It is an exposition of joint work with S.
Doplicher, K. Fredenhagen, and Gh. Piacitelli [1]. The violation of unitarity
found in quantum field theory on noncommutative spacetimes in the context of
the so-called modified Feynman rules is linked to the notion of time ordering
implicitely used in the assumption that perturbation theory may be done in
terms of Feynman propagators. Two alternative approaches which do not entail a
violation of unitarity are sketched. An outlook upon our more recent work is
given.
