At the convergence of organic electronics and biology, organic bioelectronics attracts great scientific interest. The potential applications of organic semiconductors to reversibly transmit biological signals or stimulate biological tissues inspires many research groups to explore the use of organic electronics in biological systems. Considering the surfaces of movable living tissues being arbitrarily curved at physiological environments, the flexibility of organic bioelectronic devices is of paramount importance in enabling stable and reliable performances by improving the contact and interaction of the devices with biological systems. Significant advances in flexible organic bioelectronics have been achieved in the areas of flexible organic thin film transistors (OTFTs), polymer electrodes, smart textiles, organic electrochemical ion pumps (OEIPs), ion bipolar junction transistors (IBJTs) and chemiresistors. This review will firstly discuss the materials used in flexible organic bioelectronics, which is followed by an overview on various types of flexible organic bioelectronic devices. The versatility of flexible organic bioelectronics promises a bright future for this emerging area.