Amorphous solids can flow over very long periods of time. Solid flow can also be artificially enhanced by creating defects, as by Ion Beam Sputtering (IBS) in which collimated ions with energies in the 0.1 to 10 keV range impact a solid target, eroding its surface and inducing formation of nanometric structures. Recent experiments have challenged knowledge accumulated during the last two decades so that a basic understanding of self-organized nano-pattern formation under IBS is still lacking. We show that considering the irradiated solid to flow like a highly viscous liquids can account for the complex IBS morphological phase diagram, relegating erosion to a subsidiary role and demonstrating a controllable instance of solid flow at the nanoscale. This new perspective can allow for a full harnessing of this bottom-up route to nanostructuring.