A scientific trend, which has emerged in recent years, is to combine the methods of quantum optics with the advances in design and preparation of various nanostructures. This innovative field of physics, arising from the achievements of modern nanotechnology, offers the possibility of both the fundamental study of light-matter interaction in unusual artificial quantum systems and the development of optoelectronic nanodevices with unique characteristics. The proposed theoretical research lies within this interdisciplinary trend and joins two different important fields of the modern physics: the first one is devoted to the quantum optics, the second deals with the carbon-based nanostructures – carbon nanotubes and graphene. The main goal of the research is to combine the efforts of four scientific teams from Britain, Iceland, Russia and Brazil in achieving the following objectives: to develop fundamentals of the interaction between carbon nanostructures and quantum light, to reveal and analyse various quantum-electrodynamics effects in carbon nanostructures, and to create a theoretical basis for using carbon nanostructures as elements of novel optoelectronic nanodevices.