The perovskite solar cells (PSCs) have emerged as an established technology during the last decade, with the record efficiency of such solar cells having increased from 3.8 % to 25.5 %. Recently, flexible perovskite solar cells (fPSCs) have received much attention from the academic and the industrial communities, owing to their potential for various niche applications, including portable electronics, wearable power sources, electronic textiles, and large-scale industrial roofing. fPSCs are lightweight, bendable, and suitable for roll-to-roll industrial production and can be integrated easily over any surface. This Review discusses the recent development of materials for fPSCs based on various flexible substrates, including plastic, metal, and other flexible substrates, as well as fiber-shaped perovskite solar cells, with a focus on the device structure, material selection for each layer, mechanical flexibility and the environmental stability of the fPSC devices. Finally, future applications and the outlook for fPSCs are also discussed.