Graphene combines unique electronic properties and surprising quantum effects with outstanding thermal and mechanical properties. Many potential applications, including electronics and nanocomposites, require that graphene be dispersed and processed in a fluid phase. Here, we show that graphite spontaneously exfoliates into single-layer graphene in chlorosulphonic acid, and dissolves at isotropic concentrations as high as approximately 2 mg ml(-1), which is an order of magnitude higher than previously reported values. This occurs without the need for covalent functionalization, surfactant stabilization, or sonication, which can compromise the properties of graphene or reduce flake size. We also report spontaneous formation of liquid-crystalline phases at high concentrations ( approximately 20-30 mg ml(-1)). Transparent, conducting films are produced from these dispersions at 1,000 Omega square(-1) and approximately 80% transparency. High-concentration solutions, both isotropic and liquid crystalline, could be particularly useful for making flexible electronics as well as multifunctional fibres.