Solar energy is one of the most popular clean energy sources and is a promising alternative to fulfill the increasing energy demands of modern society. Solar cells have long been under intensive research attention for harvesting energy from sunlight with a high power-conversion efficiency and low cost. However, the power outputs of photovoltaic devices suffer from fluctuations due to the intermittent instinct of the solar radiation. Integrating solar cells and energy-storage devices as self-powering systems may solve this problem through the simultaneous storage of the electricity and manipulation of the energy output. This review summarizes the research progress in the integration of new-generation solar cells with supercapacitors, with emphasis on the structures, materials, performance, and new design features. The current challenges and future prospects are discussed with the aim of expanding research and development in this field.