Introduction -- Part I Electronic Nanodevices Based on Graphene -- Tight-Binding Description of Graphene Nanostructures -- Graphene Nanoring as a Quantum Interference Device -- Graphene Nanoring as a Source of Spin-Polarized Electrons -- Spin-Dependent NDR in Graphene Superlattices -- Part II Electro-Optical Nanodevices -- Optical Nanoantennas with Tunable Radiation Patterns -- Electro-Optical Hysteresis of Nanoscale Hybrid Systems -- Conclusions and Prospects.

 The thesis covers a broad range of electronic, optical and opto-electronic devices and various predicted physical effects. In particular, it examines the quantum interference transistor effect in graphene nanorings; tunable spin-filtering and spin-dependent negative differential resistance in composite heterostructures based on graphene and ferromagnetic materials; optical and novel electro-optical bistability and hysteresis in compound systems; and the real-time control of radiation patterns of optical nanoantennas. The direction of the main radiation lobe of a regular plasmonic array can be changed abruptly by small variations in external control parameters. This optical effect, apart from its relevance for applications, is a revealing example of the Umklapp process and, thus, is a visual manifestation of one of the most fundamental laws of solid state physics: the conservation of the quasi-momentum to within a reciprocal lattice vector. The thesis analyzes not only results for particular device designs but also a variety of advanced numerical methods which are extended by the author and described in detail. These methods can be used as a sound starting point for further research. .