Fullerene-based electron acceptors, exemplified by [6,6]-phenyl-C60-butyric acid methyl ester ([60]-PCBM) and [6,6]-phenyl-C70-butyric acid methyl ester ([70]-PCBM), have enabled advances in organic photovoltaics (OPVs) in the last 20 years. New small molecule or polymeric electron acceptor materials are long sought to overcome the small photovoltage, poor light harvesting, high cost, poor photochemical stability and other limitations of fullerene-based OPVs. However, the performance of nonfullerene OPVs has so far remained inferior to [70]-PCBM-based polymer solar cells. Our group has developed new electron acceptor materials, derived from strong electron withdrawing moieties such as naphthalene diimide (NDI), perylene diimide (PDI) and tetraazabenzodifluoranthene diimides (BFI), which combine high electron affinity (3.5 – 4.0 eV) and optical band gaps of less than 2 eV with high unipolar field-effect electron mobilities (0.01 – 0.1 cm2/Vs). Bulk heterojunction (BHJ) polymer solar cells pairing the new nonfullerene acceptors with various donor polymers, including poly(3-hexylthiophene), thiazolothiazole-dithienosilole copolymer (PSEHTT) and benzodithiophene-thieno[3,4-b]thiophene copolymer (PBDTTT-CT), combine high open-circuit voltages (> 0.9 V) with high photocurrents to give power conversion efficiencies exceeding 6 %. Most importantly, the results of our studies provide new insights towards the rational design of nonfullerene acceptor materials to enable OPV devices that could surpass fullerene-based OPVs.