### Abstract

I am going to review the recent progress on the renormalisation programme for quantum field theories on the Moyal plane. There are now three different proofs that the noncommutative \phi^4_4-model, extended by a harmonic oscillator potential to reflect the UV/IR-entanglement, is renormalisable to all orders in perturbation theory. The behaviour of the \beta-function indicates that a rigorous construction of this model might be possible.

### Related Links

- http://www.math.uni-muenster.de/u/raimar/ - homepage