Both ATLAS and CMS recently reported an excess in the diphoton distribution at an invariant mass of 750 GeV. The aim of this talk is to discuss the phenomenological features of this excess in a model independent way. Assuming that the excess is due to a new resonance produced in s-channel, we will show how the current data already point to a very peculiar structure of the couplings of the resonance. This leads us to a simple effective lagrangian which describes the relevant physics of the resonance. We show how naturalness can be a powerful organizing principle to compare the different classes of models that can realize this effective lagrangian at low energy. On the other hand we comment on the intriguing possibility to relate the diphoton excess to Dark Matter portals.