Low-energy ion bombardment of semiconductor surfaces can lead to the self-organized growth of nanostructures or instead to ultra-smoothing, depending on experimental conditions. If controlled, ion bombardment could potentially be a broadly applicable route to inexpensive surface nanopatterning. However, despite much work in the area, fundamental questions remain about the physical mechanisms driving nanoscale surface evolution during bombardment. After reviewing the development of the field, recent time-resolved grazing-incidence small-angle x-ray scattering (GISAXS) experiments on elemental semiconductors (Si and Ge) from our group will be presented. These experiments, which utilize a facility at the National Synchrotron Light Source (NSLS) that we have developed for in-situ studies of surface and thin-film growth processes, provide direct information about the linear theory amplification factor as a function of bombardment conditions and substrate. The amplification factor describes the exponential growth of fluctuations on unstable surfaces and their exponential relaxation on stable surfaces; it provides insight into the fundamental mechanisms driving surface morphology evolution. The measured amplification factors point to a major role played by mass redistribution on the Si and Ge surfaces and place strong constraints on theoretical models attempting to explain nanoscale surface evolution during the ion bombardment process.