Since we can resolve the surface of the Sun directly, we can explore the origin of radial-velocity variations induced by individual solar surface features such as faculae/plage, sunspots and granulation. I will present my recent investigation of the radial-velocity variations of the Sun as a star, based on high-resolution HARPS spectra of reflected sunlight and simultaneous images from the Solar Dynamics Observatory. We found that faculae are the dominant source of activity-induced radial-velocity variations, via suppression of convective blueshift. We investigated possible proxies for activity-induced radial-velocity variations and found that optical lightcurves can only provide a partial representation of these signals; the full-disc magnetic flux, however, is an excellent tracer. In addition to this dataset, the HARPS-N spectrograph has been operating with a new solar telescope feed since 2015 July. I will present results from the first year observations, which show radial-velocity variations of up to 7-8 m/s. Identifying proxies for solar radial-velocity variations is key to understanding the radial-velocity variability of other Sun-like stars, and is also essential for other investigations such as exoplanet detection surveys.