The mechanical and electronic properties of two-dimensional materials make them promising for use in flexible electronics(1-3). Their atomic thickness and large-scale synthesis capability could enable the development of 'smart skin'(1,3-5), which could transform ordinary objects into an intelligent distributed sensor network(6). However, although many important components of such a distributed electronic system have already been demonstrated (for example, transistors, sensors and memory devices based on two-dimensional materials(1,2,4,7)), an efficient, flexible and always-on energy-harvesting solution, which is indispensable for self-powered systems, is still missing. Electromagnetic radiation from Wi-Fi systems operating at 2.4 and 5.9 gigahertz(8) is becoming increasingly ubiquitous and would be ideal to harvest for powering future distributed electronics. However, the high frequencies used for Wi-Fi communications have remained elusive to radiofrequency harvesters (that is, rectennas) made of flexible semiconductors owing to their limited transport properties(9-12). Here we demonstrate an atomically thin and flexible rectenna based on a MoS2 semiconducting-metallic-phase heterojunction with a cutoff frequency of 10 gigahertz, which represents an improvement in speed of roughly one order of magnitude compared with current state-of-the-art flexible rectifiers(9-12). This flexible MoS2-based rectifier operates up to the X-band(8) (8 to 12 gigahertz) and covers most of the unlicensed industrial, scientific and medical radio band, including the Wi-Fi channels. By integrating the ultrafast MoS2 rectifier with a flexible Wi-Fi-band antenna, we fabricate a fully flexible and integrated rectenna that achieves wireless energy harvesting of electromagnetic radiation in the Wi-Fi band with zero external bias (battery-free). Moreover, our MoS2 rectifier acts as a flexible mixer, realizing frequency conversion beyond 10 gigahertz. This work provides a universal energy-harvesting building block that can be integrated with various flexible electronic systems.