Over the last two decades, new forms of carbon, fullerenes, carbon nanotubes (CNT), isolated graphene flacks and more recently graphene nanoribbons (GNR) have been synthesized, manipulated and electrically connected. Their fundamental studies unravel remarkable electronic properties resulting from the electronic confinement at nano-scale and the electronic band structure of graphene. The feasibility of room temperature carbon based field effects transistors and inter-connexions have been demonstrated while their industrial integration as elementary bricks of a new nano-electronics raises severe technological issues. In this talk, I will present the 1-D electronic properties of carbon nanotubes and graphene nanoribbons. Their electronic band structures will be briefly developed as well as their expected electronic transport properties for pristine and disordered CNTs and GNRs. I will mainly focus on (magneto)-transport experiments performed on individually connected CNTs and GNRs. I will show that magneto-transport in the high magnetic field regime along with an electrostatic control of the electronic doping is an outstanding probe of the 1-D electronic band structure and its unusual magnetic field dependence. An applied magnetic field along the CNT axis induces giant quantum flux modulation of the conductance due to the periodic energy gap modulation at the charge neutrality point [1]. This so-called Aharonov-bohm effect is also an efficient tool to identify the metallicity of the external shell of a multi-walled carbon nanotube and to infer the locations of the different 1-D subbands [2]. By rotating the CNT perpendicular to the magnetic field, the energy gap of a semiconducting CNT is progressively reduced due to the onset of the first Landau level at zero energy and propagating Landau states develop at the flank of the tube [3]. Concerning (magneto)transport experiments on GNR, I will present compelling evidences of the 1D transport character in the first generation of chemically derived GNRs with smooth edges and the possibility of tuning backscattering effects by means of an external magnetic field [4]. These experiments enlighten the richness of the electronic transport measurements on an individual nano-object in presence of a large magnetic confinement.