Thin-film solar cells are an important source of renewable energy. The most efficient thin-film solar cells made with organic materials are blends of semiconducting polymers and fullerenes called the bulk heterojunction (BHJ). Efficient BHJs have a nanoscale phase-separated morphology that is formed during solution casting. This article reviews recent work to understand the nature of the phase-separation process resulting in the formation of the domains in polymer-fullerene BHJs. The BHJ is now viewed as a mixture of polymer-rich, fullerene-rich, and mixed polymer-fullerene domains. The formation of this structure can be understood through fundamental knowledge of polymer physics. The implications of this structure for charge transport and charge generation are given.