For large genus closed hyperbolic surfaces, their geometry properties may differ greatly from each other. However, for random hyperbolic surfaces of Weil-Petersson model which firstly studied by Maryam Mirzakhani, they look much more similar. In this talk, we will first recall some geometric properties on closed hyperbolic surfaces and their moduli space, and introduce the random hyperbolic surfaces of Weil-Petersson model. Then we will show some recent developments on the geometry of these Weil-Petersson random hyperbolic surfaces, aiming to describe the shape of them.