In this review, the current state of materials science and the device physics of semitransparent organic solar cells is summarized. Relevant synthetic strategies to narrow the band gap of organic semiconducting molecules are outlined, and recent developments in the polymer donor and near-infrared absorbing acceptor materials are discussed. Next, an overview of transparent electrodes is given, including oxides, multi-stacks, thin metal, and solution processed electrodes, as well as considerations that are unique to ST-OPVs. The remainder of this review focuses on the device engineering of ST-OPVs. The figures of merit and the theoretical limitations of ST-OPVs are covered, as well as strategies to improve the light utilization efficiency. Lastly, the importance of creating an in-depth understanding of the device physics of ST-OPVs is emphasized and the existing works that answer fundamental questions about the inherent changes in the optoelectronic processes in transparent devices are presented in a condensed way. This last part outlines the changes that are unique for devices with increased transparency and the resulting implications, serving as a point of reference for the systematic development of next-generation ST-OPVs.