The scanning tunnelling microscope (STM)1 relies on localized electron tunnelling between a sharp probe tip and a conducting sample to attain atomic-scale spatial resolution. In the 25-year period since its invention, the STM has helped uncover a wealth of phenomena in diverse physical systems—ranging from semiconductors2, 3 to superconductors4 to atomic and molecular nanosystems5, 6, 7, 8, 9. A severe limitation in scanning tunnelling microscopy is the low temporal resolution, originating from the diminished high-frequency response of the tunnel current readout circuitry. Here we overcome this limitation by measuring the reflection from a resonant inductor–capacitor circuit in which the tunnel junction is embedded, and demonstrate electronic bandwidths as high as 10 MHz. This 100-fold bandwidth improvement on the state of the art translates into fast surface topography as well as delicate measurements in mesoscopic electronics and mechanics. Broadband noise measurements across the tunnel junction using this radio-frequency STM have allowed us to perform thermometry at the nanometre scale. Furthermore, we have detected high-frequency mechanical motion with a sensitivity approaching 15 fm Hz-1/2. This sensitivity is on par with the highest available from nanoscale optical and electrical displacement detection techniques, and the radio-frequency STM is expected to be capable of quantum-limited position measurements.