Thin film solar cells based on Cu(In,Ga)Se2 absorber material have shown conversion efficiencies above 20% when fabricated on rigid glass substrates. On flexible substrates, challenges in deposition of high quality absorbers have for long limited the device efficiency to lower values. Nevertheless, our group recently achieved a 20.4% world record efficiency on a flexible polyimide substrate. This paper reviews the progress that has led to such high performance, while highlighting advantages and challenges of using flexible substrates to manufacture high efficiency CIGS solar cells.