The bombardment of surfaces with low-energy ion beams leads to material erosion and can be accompanied by changes in the topography. Under certain conditions this surface erosion can result in well-ordered nanostructures. Here an overview of the pattern formation on Si and Ge surfaces under low-energy ion beam erosion at room temperature will be given. In particular, the formation of ripple and dot patterns, and the influence of different process parameters on their formation, ordering, shape and type will be discussed. Furthermore, the internal ion beam parameters inherent to broad beam ion sources are considered as an additional degree of freedom for controlling the pattern formation process. In this context: (i) formation of ripples at near-normal ion incidence, (ii) formation of dots at oblique ion incidence without sample rotation, (iii) transition between patterns, (iv) formation of ripples with different orientations and (v) long range ordered dot patterns will be presented and discussed.