Graphene is a perfect two-dimensional (2D) carbon sheet in honeycomb lattice with unique, multi-faceted properties. Very recently plasmons have been identified in graphene thus opening a new research field called “graphene plasmonics” which provides a suitable alternative to noble-metal plasmonics, since the associated surface plasmons (SPs) exhibit much larger light confinement abilities and relatively long propagation distances, with the advantage of being highly tunable via electrostatic gating. Moreover graphene can be efficiently integrated in photonic nanostructures in order to increase the optical absorption in the visible and infrared regions (graphene photonics). In this paper we will illustrate some applications of graphene plasmonics and graphene photonics, reported in literature, in different research fields and we will review our recent numerical and experimental results concerning the linear and nonlinear optical response of graphene plasmonic and photonic nanostructures emphasizing their interaction in terms of absorption and optical resonances.