Transparent electronic devices formed on flexible substrates are expected to meet emerging technological demands where silicon-based electronics cannot provide a solution. Examples of active flexible applications include paper displays and wearable computers. So far, mainly flexible devices based on hydrogenated amorphous silicon (a-Si:H) and organic semiconductors have been investigated. However, the performance of these devices has been insufficient for use as transistors in practical computers and current-driven organic light-emitting diode displays. Fabricating high-performance devices is challenging, owing to a trade-off between processing temperature and device performance. Here, we propose to solve this problem by using a novel semiconducting material--namely, a transparent amorphous oxide semiconductor from the In-Ga-Zn-O system (a-IGZO)--for the active channel in transparent thin-film transistors (TTFTs). The a-IGZO is deposited on polyethylene terephthalate at room temperature and exhibits Hall effect mobilities exceeding 10 cm2 V(-1) s(-1), which is an order of magnitude larger than for hydrogenated amorphous silicon. TTFTs fabricated on polyethylene terephthalate sheets exhibit saturation mobilities of 6-9 cm2 V(-1) s(-1), and device characteristics are stable during repetitive bending of the TTFT sheet.