Graphene sheets—one-atom-thick two-dimensional layers of sp²-bonded carbon—are predicted to have a range of unusual properties. Their thermal conductivity and mechanical stiffness may rival the remarkable in-plane values for graphite (3,000 W m^-1 K^-1 and 1,060 GPa, respectively); their fracture strength should be comparable to that of carbon nanotubes for similar types of defects^1,2,3; and recent studies have shown that individual graphene sheets have extraordinary electronic transport properties^4,5,6,7,8. One possible route to harnessing these properties for applications would be to incorporate graphene sheets in a composite material. The manufacturing of such composites requires not only that graphene sheets be produced on a sufficient scale but that they also be incorporated, and homogeneously distributed, into various matrices. Graphite, inexpensive and available in large quantity, unfortunately does not readily exfoliate to yield individual graphene sheets. Here we present a general approach for the preparation of graphene-polymer composites via complete exfoliation of graphite⁹ and molecular-level dispersion of individual, chemically modified graphene sheets within polymer hosts. A polystyrene–graphene composite formed by this route exhibits a percolation threshold¹⁰ of 0.1 volume per cent for room-temperature electrical conductivity, the lowest reported value for any carbon-based composite except for those involving carbon nanotubes¹¹; at only 1 volume per cent, this composite has a conductivity of 0.1 S m^-1, sufficient for many electrical applications¹². Our bottom-up chemical approach of tuning the graphene sheet properties provides a path to a broad new class of graphene-based materials and their use in a variety of applications.