Carbon-based nano-materials, such as graphene and carbon nanotubes, represent a fascinating research area aiming at exploring their remarkable physical and electronic properties. These materials not only constitute a playground for physicists, they are also very promising for practical applications and are envisioned as elementary bricks of the future of the nano-electronics. As for graphene, its potential already lies in the domain of opto-electronics where its unique electronic and optical properties can be fully exploited. Indeed, recent technological advances have demonstrated its effectiveness in the fabrication of solar cells and ultra-fast lasers, as well as touch-screens and sensitive photo-detectors. Although the photo-voltaic technology is now dominated by silicon-based devices, the use of graphene could very well provide higher efficiency. However, before the applied research to take place, one must first demonstrates the operativeness of carbon-based nano-materials, and this is where the fundamental research comes into play. In this context, the use of magnetic field has been proven extremely useful for addressing their fundamental properties as it provides an external and adjustable parameter which drastically modifies their electronic band structure. In order to induce some significant changes, very high magnetic fields are required and can be provided using both DC and pulsed technology, depending of the experimental constraints. In this article, we review some of the challenging experiments on single nano-objects performed in high magnetic and low temperature. We shall mainly focus on the high-field magneto-optical and magneto-transport experiments which provided comprehensive understanding of the peculiar Landau level quantization of the Dirac-type charge carriers in graphene and thin graphite.