Amorphous oxide semiconductor thin film transistors (AOS TFT) have recently attracted attention as next generation display backplane materials. In this article, the current research trends and status of AOS TFTs for flexible displays are discussed. First, the degradation mechanism of AOS TFTs via bending stress is examined. In this part, we investigate how to define bending strain, i.e. how the bending stress deteriorates the TFT performance. In addition, we examine the recovery process of the mechanically degraded TFT via thermal energy. Then, we introduce various materials and structures to improve the mechanical durability of AOS TFTs. The material approach as well as the structural approach for each layer (substrate, buffer layer, electrode, active and gate insulator) are included in this paper.