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Optimization of the energy levels at the donor–acceptor interface of organic solar cells has driven their efficiencies to above 10%. However, further improvements towards efficiencies comparable with inorganic solar cells remain challenging because of high recombination losses, which empirically limit the open-circuit voltage (Voc) to typically less than 1 V. Here we show that this empirical limit can be overcome using non-fullerene acceptors blended with the low band gap polymer PffBT4T-2DT leading to efficiencies approaching 10% (9.95%). We achieve Voc up to 1.12 V, which corresponds to a loss of only Eg/q − Voc = 0.5 ± 0.01 V between the optical bandgap Eg of the polymer and Voc. This high Voc is shown to be associated with the achievement of remarkably low non-geminate and non-radiative recombination losses in these devices. Suppression of non-radiative recombination implies high external …