Atomically thin forms of layered materials, such as conducting graphene, insulating hexagonal boron nitride (hBN), and semiconducting molybdenum disulfide (MoS₂), have generated great interests recently due to the possibility of combining diverse atomic layers by mechanical “stacking” to create novel materials and devices. In this work, we demonstrate field-effect transistors (FETs) with MoS₂ channels, hBN dielectric, and graphene gate electrodes. These devices show field-effect mobilities of up to 45 cm²/Vs and operating gate voltage below 10 V, with greatly reduced hysteresis. Taking advantage of the mechanical strength and flexibility of these materials, we demonstrate integration onto a polymer substrate to create flexible and transparent FETs that show unchanged performance up to 1.5% strain. These heterostructure devices consisting of ultrathin two-dimensional (2D) materials open up a new route toward high-performance flexible and transparent electronics.