Many applications proposed for functional nanofibers require their assembly into a monolithic cellular structure. The ability to maintain structural integrity upon large deformation is essential to ensure a macroscopic cellular material that functions reliably. However, it remains a great challenge to achieve high elasticity in three-dimensional (3D) nanofibrous networks. Here, we report a strategy to create fibrous, isotropically bonded elastic reconstructed (FIBER) aerogels with a hierarchical cellular structure and superelasticity by combining electrospun nanofibers and the freeze-shaping technique. Our approach allows the intrinsically lamellar deposited electrospun nanofibers to assemble into elastic bulk aerogels with tunable porous structure and wettability on a large scale. The resulting FIBER aerogels exhibit the integrated properties of ultralow density (<30 mg cm(-3)), rapid recovery from 80% compression strain, superhydrophobic-superoleophilic wettability, and high pore tortuosity. More interestingly, the FIBER aerogels can effectively separate surfactant-stabilized water-in-oil emulsions, solely using gravity, with high flux (maximum of 8140 ± 220 L m(-2) h(-1)) and high separation efficiency, which match well with the requirements for treating the real emulsions. The synthesis of FIBER aerogels also provides a versatile platform for exploring the applications of nanofibers in a self-supporting, structurally adaptive, and 3D macroscopic form.