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 batteryless electronics, which will impact many sectors, and particularly 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 to fiber-shaped and planar-shaped solar cells, and it introduces the most recent research reports on the different types of textile solar cells, including their fabrication techniques. Finally, their current challenges and limitations with respect to their fabrication methods, and the issues encounter for their implementation and integration in novel devices, are also described.