Graphene has shown much promise as an organic electronic material but, despite recent achievements in the production of few-layer graphene, the quantitative exfoliation of graphite into pristine single-layer graphene has remained one of the main challenges in developing practical devices. Recently, reduced graphene oxide has been recognized as a non-feasible alternative to graphene owing to variable defect types and levels, and attention is turning towards reliable methods for the high-throughput exfoliation of graphite. Here we report that microwave irradiation of graphite suspended in molecularly engineered oligomeric ionic liquids allows for ultrahigh-efficiency exfoliation (93% yield) with a high selectivity (95%) towards 'single-layer' graphene (that is, with thicknesses <1 nm) in a short processing time (30 minutes). The isolated graphene sheets show negligible structural deterioration. They are also readily redispersible in oligomeric ionic liquids up to ~100 mg ml(-1), and form physical gels in which an anisotropic orientation of graphene sheets, once induced by a magnetic field, is maintained.