Graphene – a truly two-dimensional one-atom thick sheet of carbon – is a promising new material with potential applications ranging from photovoltaics to nanelectronics and photonics. Specifically, with carrier mobilities reaching up to ~106 cm2/Vs graphene is expected to become a major player in nanoelectronics serving as a high-quality thin flexible conductor. Obviously, for such applications the concentration of carrier-scattering defects has to be minimized to improve the performance of a graphene-based device. However, there is a multitude of applications where defects in fact can be beneficial as they can tailor the electronic, transport, optical and mechanical properties of graphene. Since graphene is an “all-surface” material, the effect of this tailoring on properties of graphene could be very strong, resulting in essentially new materials. An important example is a controlled chemical functionalization of graphene (graphane, halogenated graphene, graphene oxide) with the goal to tailor its electronic band structure. In my talk, I will report on our recent progress in studying the effect of various “defects” (semiconductor quantum dots, chemical groups) on electronic, optical and thermodynamic properties of graphene. Specifically, I will talk about an emerging field of graphene plasmonics and (non-) equilibrium thermodynamics of chemically functionalized graphene.