Solution-processable semiconductors offer the promise of low-cost scalable manufacturing of photovoltaics. However, increasing open-circuit voltage (Voc) without an associated loss of photocurrent density remains a challenge in many organic and hybrid organic/inorganic solar cell materials. Drawing from our recent experiments, we provide examples of different loss pathways that can affect high Voc cells containing organic semiconductors. Specifically, we highlight the complicated and complementary roles of bimolecular recombination via the triplet manifold, asymmetry between donor-to-acceptor photoinduced electron transfer, and acceptor-to-donor photoinduced hole transfer, and recombination at the electrode interface as loss mechanisms to be avoided, and we discuss design strategies for ameliorating these different losses at the same time.