  The fixed-point (FP) action in QCD, although it is local and determined by
classical equations, is difficult to parametrize well and is expensive to
simulate. But the stake is high: the FP action has scale invariant instanton
solutions, has no topological artifacts, satisfies the index theorem on the
lattice, does not allow exceptional configurations, requires no tuning to get
the pion massless and is expected to reduce the cut-off effects significantly.
An overview is given including a discussion on tests in Yang-Mills theory, QCD
and $d=2$ spin and gauge models.
