Abstract: The unique electronic properties of graphene have attracted a huge amount of attention since its discovery in 2004. The structural properties of such a two-dimensional lattice are less known but not less exceptional. Graphene has a rippled structure at any finite temperature, negative lattice expansion, is elastic up to very large deformations but displays many anharmonic effects, has a peculiar phonon spectrum and melts in a very unusual way. The structural properties of graphene are rather well described by bond order classical potentials. We have shown in the past years that Monte Carlo simulations based on such a potential (LCBOPII) can provide a detailed picture of the structure of graphene and of the thermal long wavelength behaviour due to rippling and have compared our findings to continuum models developed to describe two-dimensional membranes . The advantage of classical simulations is the ability to deal with very large samples, allowing the study of localized (vacancies) and extended defects (grain boundaries), melting, strain and frictional behavior.  Examples will be shown in this talk.