Grapheme and graphene-related systems have been the focus of intensive research due to their exceptional electronic behavior. Their properties have been studied for decades, from the unique band structure predicted for a single layer of graphite, to the unexpected linear magnetoresistance observed in its bulk form. Since its experimental isolation in 2004, studies on graphene monolayer, bilayer, and few-layer systems garnered an overwhelming amount of attention from the scientific community, with studies focusing on multilayers with nanometer thicknesses paling in comparison. The main motivation of this study is to further the understanding of systems consisting of multilayer graphene and ultrathin graphite (graphitic multilayers) through electron transport experiments. Uniquely designed and fabricated devices based on carbon nanostructures were used to study the transport of charge carriers under high electric and magnetic fields. For short-channel suspended graphitic multilayer devices, the two-terminal differential conductance dI/dV as a function of drain-source bias V_d displays a pronounced dip pinned at V_d=0, explained by the hot electron effect. The dip is attenuated under high magnetic fields, likely due to intra-Landau level cyclotron phonon scattering. Also, distinct high-energy dI/dV anomalies have been observed and shown to be related to intrinsic phonon-emission processes in graphite. The evolution of such dI/dV anomalies under magnetic fields is understood as a consequence of the inter-Landau level cyclotron-phonon resonance scattering. The magnetoresistance (MR) of this system shows Shubnikov-de Haas oscillations on top of a strong positive nearly-linear background. Upon the introduction of a significant amount of short-range disorders through ion implantation, the positive MR transforms into a negative MR. The results for the MR of pure and implanted graphitic multilayers can be understood by considering a recent magneto-transport theory for two-dimensional systems. Four terminal measurements on unique multi-terminal devices with suspended multilayer graphene grown by ambient-pressure chemical vapor deposition also display the dI/dV dip related to the hot electron effect, and its attenuation at high magnetic fields, confirming its intrinsic nature for multilayer graphene systems.