Perturbative series are asymptotic, so at fixed coupling, there is an
order at which the accuracy starts decreasing. It is not clear that
the fourth order correction for the hadronic width of the Z will
improve the third order accuracy. The culprit are the large field
configurations in the path integral and the solution is their
judicious removal. I discuss three examples where this issue is well
undestood and multiloop calculations are possible: quantum mechanics,
scalar field theory and lattice QCD in the quenched approximation.  I
discuss recent attempts to write modified Feynman rules to automatize
this procedure.