Hybrid heterojunction solar cells based on silicon and single-walled carbon nanotube (SWCNT) thin films have a simple structure and their manufacture employ simple low-temperature processes. Moreover, their progress has been rapid during the last decade, wherein the efficiency of heterojunction solar cells combining hydrogenated amorphous silicon (a-Si:H) and SWCNTs thin film has increased from 0.03% to 8.80%. Here, we present a comprehensive overview of the state-of-the-art on SWCNTs/a-Si:H heterojunction solar cells. In addition to a comprehensive technology review, important special features such as adhesion of SWCNT film to a-Si:H, the interface between SWCNT and a-Si:H, and their influence on the performance of the heterojunctions are included. Future paths for improving the performance of such solar cells are also suggested. Finally, key challenges and trends for further research and development of SWCNTs/amorphous silicon heterojunction solar cells are discussed. This article is categorized under: Photovoltaics > Science and Materials.