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 cm(2)/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.