A new class of conjugated polymers with high charge mobilities exhibits the apparently conflicting morphological features of increased order at the molecular scale while lacking long-range order and crystallinity. To exploit their unique properties, mechanistic insights for charge transport events taking place from the molecular to the device scale must be uncovered. Thus, a central contributor to the continued progress in conjugated optoelectronic materials will be the development of advanced characterization tools, particularly those targeted to measuring the charge-transfer processes in heterogeneous, anisotropic, and hierarchically structured materials. This feature article describes the morphological properties that make partially ordered polymers an intriguing materials system to explore connections between chemical identity, solid-phase microstructure, and hierarchical charge transport. To this end, recent directions in materials development and new opportunities for characterization are discussed.