Solar cells based on chalcopyrite Cu(In, Ga)Se2 (CIGS) absorber layers show the highest potential for low-cost solar electricity by yielding comparable efficiencies to polycrystalline Si wafer-based cells, while also offering inherent advantages of thin-film technology for cost reduction. Highest efficiency of 20.3% was recently achieved on rigid glass substrate. Deposition of CIGS films onto flexible substrates opens new fields of applications and could significantly decrease production costs by employing roll-to-roll manufacturing and monolithic integration of solar cells to develop modules. Whereas, some years back, it seemed difficult to reach performance levels on flexible substrates similar to that obtained on glass, recent results on flexible polyimide prove that the efficiency gap can be significantly reduced. Different materials, i.e., mostly metals or plastics, have been used as flexible substrates, with highest cell efficiency of 18.7% demonstrated on a polyimide film. Improvements in efficiencies of flexible solar cells and modules achieved over the past few decades are discussed in this paper, addressing the main characteristics of substrate materials. The technology transfer from laboratory research to large-scale industrial production of CIGS modules leads to new manufacturing challenges, mainly for CIGS deposition, interconnections of cells, and long-term performance stability.