Abstract: Following the unpublished work of C. Rezk, Toposes and Homotopy Toposes, we present a formulation of the notion of model topos, intended as a model-categorical version of the classical concept of Grothendieck topos. Such a definition will be sensible enough to establish a Giraud-type theorem for model topoi. We will start by reviewing the notion of Grothendieck topos, albeit from a slightly unusual perspective which avoids the use of Grothendieck topologies. We will then state one of the possible formulation of the classical Giraud's theorem for Grothendieck topoi which characterises them axiomatically as categories satisfying suitable internal properties. An important role in this result is played by the concept of weak descent. Using our definition of Grothendieck topoi and its equivalent interpretation which involve categories admitting a left exact small presentation, it will be relatively easy to explain how to homotopify the ordinary categorical setting (substituting presheaves categories with simplicial presheaves categories and localizations with Bousfield localizations) and get the desired notion of model topoi. We will finally state and sketch the proof of a meaningful version of Giraud's theorem for such model topoi and, if time permits, we will see how it applies to provide a nice class of examples of model topoi which present the homotopy theory of homotopy sheaves on a Grothendieck site.