The power conversion efficiencies (PCEs) of single-junction organic solar cells (OSC) have now reached over 18%. This rapid recent progress can be attributed to the development of new nonfullerene electron acceptors (NFAs) that are paired with suitable high performing polymer electron donors. Substantial improvements in the PCEs and long-term stability enabled by NFA OSCs have allowed the development and integration of these systems into many niche and novel applications. Here, the recent progress that has been made in understanding the device photophysics of high performing polymer:NFA blends is highlighted. As the bulk heterojunction morphology is intrinsically linked to the device photophysics, this review focuses on studies that have provided noteworthy morphological insights using advanced techniques such as solid-state NMR and resonant soft X-ray scattering. Through this, some of the major challenges that must be overcome to attain PCEs of over 20% in NFA OSCs are addressed.