Current research on graphene, a 2D hexagonal structure of carbon atoms, is presented. The structural features of and basic methods for obtaining graphene are discussed. The phononic properties of graphene and their dependent graphene characteristics are examined. In particular, how to measure the thermal conductivity of graphene is discussed and recent experimental and theoretical advances on this subject are described. The stability problems of 2D crystal structures are addressed and the dimensional effects in the dependence of graphene characteristics on the lateral size are discussed. Simulation methods for determining the phononic characteristics and thermal conductivity of graphene are reviewed.