Strongly coupled QED

A short review of some of the most relevant contributions to non-perturbative QED is done. Since the numerical data, if correctly analyzed, rule out a Gaussian behaviour of strongly coupled QED a la lambda phi(4), 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.