Strongly Coupled QED

A short review of some of the most relevant contributions to non-perturbative QED is done. Since a Gaussian behaviour of QED `a la $\lambda {\varphi }^4$ 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.