  A new version of scale analysis and renormalization theory has been found on
the non-commutative Moyal space. It could be useful for physics beyond the
standard model or for standard physics in strong external field. The good news
is that quantum field theory is better behaved on non-commutative than on
ordinary space: indeed it has no Landau ghost. Noncommutativity might therefore
be an alternative to supersymmetry. We review this rapidly growing subject.
