As an alternative to polymer membranes, ultrathin free-standing single-walled carbon-nanotube network films are used to realize oil/water separation with ultrahigh flux. The films with tunable thickness of the tens of nanometer scale can effectively separate both micrometer and nanometer-sized surfactant-free and surfactant-stabilized water-in-oil emulsions with a flux 2-3 orders of magnitude higher than commercial filtration membranes with similar separation performance.