During the last few years, textile solar cells with planar and fiber-shaped configurations have attracted enormous research interest. These flexible-type solar cells have a huge potential applicability in self-powered and battery-less electronics, which will impact many sectors, and particularly the Internet of Things. Textile solar cells are lightweight, super-flexible, formable, and foldable. Thus, they could be ideal power-harvester alternatives to common flexible solar cells required in smart textiles, electronic textiles, and wearable electronic devices. This review presents a brief overview on fiber-shaped and planar-shaped solar cells, and it introduces the most recent research reports on the different types of textile solar cells, including details on their fabrication techniques. It also addresses the current challenges and limitations of their technology development, and the encountered issues for their future application and integration in novel devices.