Thin-film flexible photovoltaics are paving the way to low-cost electricity. Organic, inorganic and organic-inorganic solar cells are deposited over flexible substrates by high-throughput (often roll-to-roll printing) technologies to afford lightweight, economic solar modules that can be integrated into, not installed on, various surfaces. Current conversion efficiencies under standard conditions are in the 3-15 % range, but in real applications the overall productivity is high. These new photovoltaic technologies are ready to provide cheap, clean electricity to the 2 billion people who lack access to the grid as well as to energy-eager companies and families in the developed world facing the increasing costs of electricity generated using fossil fuel resources. This Review focuses on recent achievements in the area of flexible solar cells, highlights the principles behind the main technologies, and discusses future challenges in this area.