With transistors set to reach their smallest possible size in the next decade, the silicon chip is likely to change dramatically, or be replaced entirely. The transistor industry's path which has been largely shaped by Gordon Moore's famous prediction that the number of transistors on a silicon chip would double approximately every eighteen months, predicts a size of transistor which silicon technology cannot sustain, thereby ushering in a post-silicon age in semiconductors soon. In this scenario, graphene-derived nanomaterials are emerging as promising candidates for post-silicon electronics devices, with potential applications as atomically thin transistors and other nanoelectronic devices which incorporate quantum size effects. However, such claims still require a few important issues to be addressed first . This thesis focuses on demonstrating and studying field effect behaviour in graphene- and graphite-based devices. It describes the differences between the two types of graphene bilayers and the effect of their stacking order when placed in an electric field. The differences are studied using Scanning Photocurrent Microscopy, leading to the conclusion that the bottom layer in a misoriented bilayer effectively screens the charge carrier modulation when used in a back-gated FET configuration. A polymer electrolyte gate was employed on top to ultilise the enhanced carrier mobility within the top layer. The study is extended from bilayer graphene to multilayer graphene (graphite) while addressing a possibility of fabricating a field effect transistor on such a material. The thesis comments on the differences between each of these and their prospects in future applications. While emphasizing the effect of the substrate in such FETs, an intrinsic gain in a graphene-based FET of over one is shown at room temperature. The importance of both these aspects in the devices is also elucidated. Furthermore, the misoriented bilayer transistors were incorporated into phase-shift detectors, to exhibit their functioning in logical circuits. On the technical side, a novel method for fabricating graphene-based transistors on a lab-scale has been demonstrated which uses fluorescence quenching to distinguish the number of layers in a graphene stack.