In the last years there has been a great progress toward the understanding of the general structure of mean field spin glass models, on rigorous basis. In particular, it has been proved that the free energy is in fact given through the Parisi representation, in the infinite volume limit. Moreover, the full ultrametricity of overlap distributions seems to be in the reach.
The purpose of this talk is to give a review of methods and results, in the frame of a very simple and elementary presentation. The talk is intended for a general audience, and we stress general structural aspects, rather than purely technical topics.

Department of Physics, University of Rome “La Sapienza”andINFN, Section of Rome