This review covers methods to measure key aspects of nanoscale structure in organic photovoltaic devices based on polymer-fullerene bulk heterojunctions. The importance of nanoscale structure to the power conversion efficiency and stability of these devices has been recognized, but robust correlations have yet to emerge despite a significant community-wide research investment. Our perspective is that more uniform selection, execution, and interpretation of nanoscale structure measurements will accelerate this endeavor. We will discuss organic bulk heterojunction structural measurements of contemporary interest and importance including vertical stratification, molecular orientation and order, and nanoscale morphology. Specific recommendations are made regarding the technical implementation of some popular techniques, with an eye toward the elimination of artifacts, ambiguous data, and misinterpretation. When possible, topics are highlighted where there is a community consensus on the results of nanoscale structure measurements and how they may relate to organic photovoltaic device performance.