All-perovskite polycrystalline thin-film tandem solar cells, which consist of a wide-bandgap (WBG) perovskite front cell and a narrow-bandgap (NBG) perovskite rear cell, hold great promise to deliver power conversion efficiency over 30% while maintaining low manufacturing cost. With only a few years' development, efficiencies over 25% have been demonstrated in both 4-terminal and 2-terminal all-perovskite tandem solar cells. Currently, the majority of the all-perovskite tandems are fabricated on rigid glass substrates. To unlock the full potential of thin film tandems, it is highly desirable to develop all-perovskite tandem solar cells on flexible and lightweight substrates. This would open up the possibilities for high throughput roll-to-roll manufacturing and various attractive applications including the portable and wearable electronics, smart buildings, transportations, etc., where a combination of high efficiency, lightweight, and flexibility are important considerations. In this contribution, we developed highly efficient near-infrared transparent (NIR) WBG perovskite and NBG perovskite solar cells on flexible and lightweight polymer foils, and demonstrated over 22% flexible all-perovskite tandem solar cells in 4-terminal configuration.