Solution processed thin-film solar technologies, such as organic photovoltaics, and more recently, perovskite solar cells, may provide low-cost electricity generation. These technologies suffer from insufficient light absorption due to thin absorber layers. Plasmonic nanostructures have been incorporated in both technologies, initially with the aim of increasing light absorption, but reports have also shown significant enhancement in electrical characteristics in devices. Enhancement mechanisms that are facilitated by plasmonic nanostructures such as improved exciton dissociation and charge carrier transport, can occur concurrently with improved light absorption. This work surveys the myriad enhancement mechanisms and, importantly, discusses the extent of current understanding, as well as insights gained in plasmonics applications thus far. Given the substantial opportunities, the continuous focus on characterization and interpretation of enhancement mechanisms is imperative to unlock the full potential of plasmonic organic and perovskite solar cells. In particular, electrical or electronic effects from plasmonic nanostructure integration deserves further attention as a promising complement to improvements in device performance from optical effects.