With the rapid advancement of non-fullerene acceptors (NFAs), the power conversion efficiency (PCE) of organic solar cells (OSCs) has surpassed the 20% threshold, highlighting their considerable potential as next-generation energy conversion devices. In comparison to inorganic or perovskite solar cells, the open-circuit voltage (Voc) of OSCs is constrained by substantial non-radiative energy losses (ΔEnr), leading to values notably below those anticipated by the Shockley-Queisser limit. In OSCs, non-radiative energy losses are intimately associated with the electroluminescent quantum efficiency (EQEEL) of charge transfer states, which is in turn directly affected by the photoluminescence quantum yield (PLQY) of acceptor materials. Consequently, enhancing the PLQY of low-bandgap acceptor materials has emerged as a pivotal strategy to effectively mitigate ΔEnr. This review article delves into the intrinsic correlation between molecular structure and PLQY from the vantage point of acceptor material design. It further explores methodologies for designing acceptor materials exhibiting high PLQY, with the ultimate goal of realizing OSCs that combine high efficiency with minimal ΔEnr.