Graphene is a stable crystalline membrane. Since its discovery in 2004, it constitutes the main benchmark for the emergent technology of 2D materials. Along with its peculiar electronic properties, it presents a rich mechanical phenomenology that so far is not completely understood. Experimental results using Transmission Electron Microscopy show how the equilibrium state of a suspended graphene monolayer presents corrugations (ripples). Other recent experiments use Scanning Tunneling Microscopy to promote stable buckling of suspended graphene monolayers or to track height fluctuations showing non gaussian velocity distributions. All these experimental results make it necessary to develop a theoretical framework that can combine elasticity of a suspended membrane with some internal degrees of freedom that can give rise to these non trivial behaviors.

In this talk I will present different theoretical approaches that try to account for these effects and allow us to address the equilibrium behavior of the graphene monolayer as much as its out of equilibrium dynamics.