Organic solar cells benefit from non‐fullerene acceptors (NFA) due to their high absorption coefficients, tunable frontier energy levels, and optical gaps, as well as their relatively high luminescence quantum efficiencies as compared to fullerenes. Those merits result in high yields of charge generation at a low or negligible energetic offset at the donor/NFA heterojunction, with efficiencies over 19% achieved for single‐junction devices. Pushing this value significantly over 20% requires an increase in open‐circuit voltage, which is currently still well below the thermodynamic limit. This can only be achieved by reducing non‐radiative recombination, and hereby increasing the electroluminescence quantum efficiency of the photo‐active layer. Here, current understanding of the origin of non‐radiative decay, as well as an accurate quantification of the associated voltage losses are summarized. Promising strategies for suppressing these losses are highlighted, with focus on new material design, optimization of donor–acceptor combination, and blend morphology. This review aims at guiding researchers in their quest to find future solar harvesting donor–acceptor blends, which combine a high yield of exciton dissociation with a high yield of radiative free carrier recombination and low voltage losses, hereby closing the efficiency gap with inorganic and perovskite photovoltaics.