QED at strong coupling

One of the most fundamental questions in field theory is whether QED has a non-trivial continuum limit. In this talk I shall review recent lattice work which addresses this problem. The key-issue is the determination of the renormalization group flow and the derivation of the Callan-Symanzik β-function. The β-function does not show an ultra-violet stable zero, but is consistent with the prediction of renormalized perturbation theory. This indicates triviality. The question to what extent QED is a valid low-energy theory is raised. Furthermore, the anomalous dimension and the critical exponents of the fermion mass operator are examined. (orig.)