Résumé : We shall survey recent progress towards the understanding of the geometry of random hyperbolic surfaces and random maps (both in low and high genus). We will in particular try to highlight similarities between a few constructions on both theories. The talk will be based on joint works in progress with Timothy Budd on one side and Thomas Budzinski & Bram Petri on the other side.

Keywords : Random triangulations; random maps; random hyperbolic surfaces; Weil-Peterson