  A short review of some of the most relevant contributions to non-perturbative
QED is done. Since a Gaussian behaviour of QED \`a la $\lambda\phi^4$ has been
ruled out by the numerical data, I analyse the other two most reliable
scenarios, i.e. triviality \`a la Nambu-Jona Lasinio and non-Gaussian critical
behaviour. I give a suggestive theoretical argument against a Gaussian
behaviour of QED \`a la Nambu-Jona Lasinio, and show how the numerical data for
the susceptibility at the critical point of QED support this result.
