Doctor of Philosophy / Department of Chemical Engineering / Vikas Berry / Graphene - a single atom thick two dimensional sheet of sp[superscript]2 bonded carbon atoms arranged in a honeycomb lattice - has shown great promise for both fundamental research & applications because of its unique electrical, optical, thermal, mechanical and chemical properties. Derivatization of graphene unlocks a plethora of novel properties unavailable to their pristine parent “graphene”. In this dissertation we have synthesized various structural and chemical derivatives of graphene; characterized them in detail; and leveraged their exotic properties for diverse applications. We have synthesized protein/DNA/ethylenediamine functionalized derivatives of graphene via a HATU catalyzed amide reaction of primary-amine-containing moieties with graphene oxide (GO) – an oxyfunctional graphene derivative. In contrast to non-specificity of graphene, this functionalization of GO has enabled highly specific interactions with analytes. Devices fabricated from the protein (concanavalin – A) and DNA functionalized graphene derivatives were demonstrated to enable label-free, specific detection of bacteria and DNA molecules, respectively, with single quanta sensitivity. Room temperature electrical characterization of the sensors showed a generation of ~ 1400 charge carriers for single bacterium attachment and an increase of 5.6 X 10[superscript]12 charge carriers / cm[superscript]2 for attachment of a single complementary strand of DNA. This work has shown for the first time the viability of graphene for bio-electronics and sensing at single quanta level. Taking the bio-interfacing of graphene to the next level, we demonstrate the instantaneous swaddling of a single live bacterium (Bacillus subtilis) with several hundred sq. micron (~ 600 µm[superscript]2) areal protein-functionalized graphene sheets. The atomic impermeability and high yield strength of graphene resulted in hermetic compartmentalization of bacteria. This enabled preservation of the dimensional and topological characteristics of the bacterium against the degrading effects of harsh environments such as the ultrahigh vacuum (~ 10[superscript]-5 Torr) and high intensity electron beam (~ 150 A/cm[superscript]2) in a transmission electron microscope (TEM) column. While an unwrapped bacterium shrank by ~ 76 % and displayed significant charge buildup in the TEM column; a wrapped bacterium remained uncontracted and undamaged owing to the graphenic wraps. This work has shown for the first time an impermeable graphenic encasement of bacteria and its application in high vacuum TEM imaging without using any lengthy traditional biological TEM sample preparation techniques. In an inch-scale, we fabricated robust free-standing paper composed of TWEEN/Graphene composite which exhibited excellent chemical stability and mechanical strength. This paper displayed excellent biocompatibility towards three mammalian cell lines while inhibiting the non-specific binding of bacteria (Bacillus cereus). We predict this composite and its derivatives to have excellent applications in biomedical engineering for transplant devices, invasive instrument coatings and implants. We also demonstrate a novel, ultra-fast and high yield process for reducing GO to reduced graphene oxide (RGO) using a facile hydride-based chemistry. The RGO sheets thus-produced exhibited high carrier mobilities (~ 100-600 cm[superscript]2/V•s) and reinstatement of the ambipolar characteristic of graphene. Raman spectra and UV-Vis spectroscopy on the RGO sheets displayed a high degree of restoration of the crystalline sp2 lattice with relatively low defects. We fabricated graphene nanoribbons (GNRs) – 1D structural derivatives of graphene – using a nano-scale cutting process from highly oriented pyrolytic graphite (HOPG) blocks, with widths pre-determinable between 5 nm to 600 nm. The as-produced GNRs had very high aspect ratio in the longitudinal direction (~ 0.01); exhibited predominantly mono-layered structure (< 10 % bilayer); and smooth edges (Raman I[subscript]D/G ~ 0.25 -0.28). Low temperature electrical transport measurements on back-gated thin film GNR devices were performed and a carrier mobility of ~ 20 ± 4 cm[superscript]2/V•s with sheet resistances of 2.2-5.1 MΩ / □ was extracted. Despite the ~ 50 nm thicknesses of the films, a clear bandgap scaling was observed with transport via variable range hopping (VRH) in 2 and 3 dimensions. This work demonstrates the first fully functional narrow pristine GNR thin-film field effect transistors (FETs). In addition we fabricated graphene quantum dots (GQDs) – 0D derivatives of graphene with dimensions < 100 nm – using a slight variation of our nano-scale cutting strategy, where the cleavage process is carried out in two dimensions. A high degree of control on the dimensions (Std. Dev. of ~ 5 nm for 50 X 50 nm square GQDs) and shape (pre-determinable between square, rectangle, triangle and trapezoid) of the as-synthesized GQDs is demonstrated. The optical properties of the GQDs such as the UV-Vis absorbance and photoluminescence were studied and their facile tunability was demonstrated depending on their dimensions. This work demonstrates for the first time the high throughput fabrication of GQDs with tunable dimensions and shape.