Polymer-based composites were heralded in the 1960s as a new paradigm for materials. By dispersing strong, highly stiff fibres in a polymer matrix, high-performance lightweight composites could be developed and tailored to individual applications(1). Today we stand at a similar threshold in the realm of polymer nanocomposites with the promise of strong, durable, multifunctional materials with low nanofiller content(2-11). However, the cost of nanoparticles, their availability and the challenges that remain to achieve good dispersion pose significant obstacles to these goals. Here, we report the creation of polymer nanocomposites with functionalized graphene sheets, which overcome these obstacles and provide superb polymer-particle interactions. An unprecedented shift in glass transition temperature of over 40 degrees C is obtained for polyacrylonitrile) at 1 wt% functionalized graphene sheet, and with only 0.05 wt% functionalized graphene sheet in poly methyl methacrylate) there is an improvement of nearly 30 degrees C. Modulus, ultimate strength and thermal stability follow a similar trend, with values for functionalized graphene sheet - poly methyl methacrylate) rivaling those for single-walled carbon nanotube-poly methyl methacrylate) composites.