QED: Chiral transition and the issue of triviality

I give a review and progress report on studies of lattice QED. I emphasize analytical results and methods that are applied in data analysis. Also, I derive some bounds for the critical exponents and establish their connection with scaling violations. Triviality, as realized in $\phi^4$ theory, is ruled out on theoretical grounds. I show that the present data, if analyzed correctly, all lead to the same conclusions. They are compatible with power law scaling with nongaussian exponents.