Recent advances in two-dimensional semiconductors, particularly molybdenum disulfide (MoS2), have enabled the fabrication of flexible electronic devices with outstanding mechanical flexibility. Previous approaches typically involved the synthesis of MoS2 on a rigid substrate at a high temperature followed by the transfer to a flexible substrate onto which the device is fabricated. A recurring drawback with this methodology is the fact that flexible substrates have a lower melting temperature than the MoS2 growth process, and that the transfer process degrades the electronic properties of MoS2. Here we report a strategy for directly synthesizing high-quality and high-crystallinity MoS2 monolayers on polymers and ultrathin glass substrates (thickness ~30 µm) at ~150 °C using metal–organic chemical vapour deposition. By avoiding the transfer process, the MoS2 quality is preserved. On flexible field-effect transistors, we achieve a mobility of 9.1 cm2 V−1 s−1 and a positive threshold voltage of +5 V, which is essential for reducing device power consumption. Moreover, under bending conditions, our logic circuits exhibit stable operation while phototransistors can detect light over a wide range of wavelengths from 405 nm to 904 nm.