Graphene, being the first 2D material available to us, has triggered tremendous interests across a broad range of areas. For every successful demonstration of a novel graphene-based device, a question often asked is what would be changed if the dimensions of graphene are reduced? In an effort to answer it, this thesis systematically studies the size effects on the electron and spin transport properties of graphene: two of the fundamental aspects of graphene-based electronic devices. Two types of devices: graphene field-effect transistors and graphene lateral spin-valves were manufactured by top-down nanofabrication. With the operating parameters for each fabrication and characterisation technique optimised, the synthesis of graphene ribbons of widths from several micrometres down to 16 nm has been achieved. A solution-based protocol has also been developed to effectively remove polymer residues from the graphene surface using inorganic solvents. Optimal device performance was realised by comparing the cleaning effectiveness between different solutions, employing surface and electrical characterisation. The width dependence of the resistivity of graphene nanoribbons was studied via field-effect transistors. The experimental data of resistivity versus width was well fitted by a quantum model which assumes ballistic transport in graphene but diffusive scattering at the edges. From this model, the electron mean free path for conduction was extracted to be between 50 and 200 nm, agreeing with reported values. Another important finding reveals that the charge carrier density in graphene nanoribbons was also width dependent, and that at a certain width the doping switched polarity from p-type to n-type. Graphene lateral spin-valves were fabricated with e-beam evaporated TiO2 as the pinhole-free and less resistive tunnel barriers that doped the graphene channels for spin transport n-type. Narrower graphene channels had lower charge carrier density in them and gave rise to larger contact resistance which scaled inversely with the width. Non-local measurements of a remaining device demonstrated spin transport signals but also suffered from noise and domain wall pinning caused by the sample processing steps prior to the measurements.