Nanoscale "quantum dot" structures can localize electrons and holes, for device applications ranging from lasers to memory. However, the desired size range is beyond the reach of semiconductor lithography. In epitaxial systems (e.g. Ge films grown on Si), misfit stress can drive self-assembly and even spatial self-organization of nanoscale dots. The possibility of replacing lithography with self-assembly has generated broad interest; but a detailed understanding of the growth and properties of such self-assembled dots is only beginning to take shape.