Appears in collection : Random Geometry / Géométrie aléatoire

In this talk we consider large Boltzmann stable planar maps of index $\alpha\in (1,2)$, We will show that this model converges in the scaling limit towards a random compact metric space that we construct explicitly. We will also present some results concerning the topology and the geodesics of the scaling limit. This talk is based on a joint work with Nicolas Curien and Grégory Miermont.