The formation of periodic ripple structures on surfaces bombarded with ions at oblique (off-normal) incidence is a well-known and intensely studied phenomenon. In contrast to these long standing investigations, a new self-organization phenomenon can be observed for ion sputtering at oblique ion incidence with simultaneous sample rotation, where the formation of nanometer-sized islands (dimension < 100 nm) can be observed. For prolonged sputtering, these island or dot structures are characterized by relatively uniform size distribution and a remarkable large degree of spatial ordering. This contribution focuses on the specific role of both ion incidence angle and temperature on the dimension, geometrical shape and the spatial arrangement of the arising nanostructures during low-energy ion sputtering. Scanning force microscopy (AFM) and high-resolution transmission electron microscopy (HRTEM) are used to investigate the evolution of the surface topography and morphology of these self-organized crystalline nanostructures. Depending on the ion incidence and temperature, these nanostructures show hexagonal or square ordering with conical or sinusoidal shape. New experimental results for dot formation on InP, GaSb, InSb and InAs surfaces will be presented.