In the last few decades, advances and breakthroughs of carbon materials have been witnessed in both scientific fundamentals and potential applications. The combination of carbon materials with traditional silicon semiconductors to fabricate solar cells has been a promising field of carbon science. The power conversion efficiency has reached 15-17% with an astonishing speed, and the diversity of systems stimulates interest in further research. Here, the historical development and state-of-the-art carbon/silicon heterojunction solar cells are covered. Firstly, the basic concept and mechanism of carbon/silicon solar cells are introduced with a specific focus on solar cells assembled with carbon nanotubes and graphene due to their unique structures and properties. Then, several key technologies with special electrical and optical designs are introduced to improve the cell performance, such as chemical doping, interface passivation, anti-reflection coatings, and textured surfaces. Finally, potential pathways and opportunities based on the carbon/silicon heterojunction are envisaged. The aspects discussed here may enable researchers to better understand the photovoltaic effect of carbon/silicon heterojunctions and to optimize the design of graphene-based photodevices for a wide range of applications.