In this work, we report an ultra-high enhancement of 4030% in thermal conductivity of polyetherimide/graphene nanocomposite (k = 9.5 Wm-1K-1) prepared through the use of expanded graphite (EG) with hydrogen peroxide as an intercalating agent at 10 weights% composition (k of pure polyetherimide ~ 0.23 Wm-1K-1). This value represents the highest thermal conductivity ever measured in a polymer composite at this low filler loading and is more than a factor of 2 higher relative to earlier reported results. This ultra-high thermal conductivity value is found to be due to an expanded graphite mediated interconnected graphene network throughout the composite, establishing a percolative environment that enables highly efficient thermal transport in the composite. Comparative studies were also performed using sodium chlorate as an intercalating agent. At 10 wt% composition, sodium chlorate intercalated expanded graphite was found to lead to a smaller enhancement of 2190% in k of composite. These results highlight the distinct advantage of hydrogen peroxide as an intercalating agent in enhancing thermal conductivity. Detailed characterization performed to elucidate this advantage, revealed that hydrogen peroxide led to primarily edge oxidation of graphene sheets within expanded graphite, leaving the basal plane intact, thus preserving the ultra-high in-plane thermal conductivity of ~ 2000 Wm-1K-1. Sodium chlorate, on the other hand, led to a higher degree of oxidation, with a large number of oxygen groups on basal plane of graphene, dramatically lowering its in-plane thermal conductivity. To directly shed light on the effect of intercalating agents on thermal conductivity of graphene itself, we prepared expanded graphite paper by compressing expanded graphite particles together. Thermal diffusivity of hydrogen-peroxide prepared expanded graphite paper was measured to be 9.5 mm2/s while that of sodium chlorate case measured to be 6.7 mm2/s, thus directly confirming the beneficial impact of hydrogen peroxide on k of graphene itself. This study is the first to address the role of intercalating agents on k of expanded graphite/polymer composites and has led to the discovery of hydrogen peroxide as an effective intercalating agent for achieving ultra-high thermal conductivity values. The work is also the first to address the comparison between edge and basal plane functionalization of graphene for enhancement of k of graphene-nanoplatelet /polyetherimide (GnP/PEI) composites. Graphene nanoplatelets (GnPs) comprise of multiple layers of graphene stacked parallel to each other. Edge functionalization enables the advantage of coupling the edges of all sheets of GnP with the embedding polymer, thus enabling the entire nanoplatelet to efficiently conduct heat through the composite. Basal-plane functionalization only couples the outermost layers of GnP with the polymer, thus causing only part of the nanoplatelet to be effective in conducting heat. Another very important advantage of edge-functionalization lies in leaving the basal plane of graphene intact. This preserves the ultra-high in-plane k of graphene (k~ 2000 Wm-1K-1). Basal plane functionalization, on the other hand, introduces a large number of defects in the basal plane of graphene dramatically lowering its intrinsic k value. Molecular dynamics simulations have revealed that even 5% functionalization of the basal plane can lower graphene thermal conductivity by as much as 90%. In this work, we experimentally realized the outlined advantages of edge-functionalization on the enhancement of k. Edge functionalization was achieved by oxidizing graphene with an excess of carboxyl groups through use of sulfuric acid, sodium chlorate and hydrogen peroxide. Carboxyl groups are known to preferentially attach to edges of graphene leading to edge oxidation. Basal plane oxidation was achieved through Hummer’s method by using sulfuric acid and potassium permanganate. Measurements reveal edge-oxidized graphene to enhance composite k by 18%, while basal-plane oxidized graphene reduced composite k by 57% at 10 wt% composition, clearly outlining the advantage of edge-functionalization on enhancement of thermal conductivity. Detailed characterization was performed to confirm edge versus basal plane oxidation. X-ray photoelectron spectroscopy showed greater fraction of carboxyl groups in edge-oxidized graphene, while basal plane oxidized graphene had larger fraction of hydroxyl/epoxy oxygen groups. 2D Raman mapping was used to obtain ID/IG ratios separately on edge and basal plane of GnPs. Edge oxidized graphene demonstrated higher ID/IG ratio on edge, while basal plane oxidized graphene demonstrated higher ID/IG ratio on basal plane. These studies for the first time, comprehensively demonstrate that edge functionalization can lead to superior thermal conductivity enhancement. Unique breakthroughs outlined in this thesis will lead to promising new avenues to achieve next-generation ultra-high thermal conductivity polymer-graphene nanocomposites.