With the current development of electron beam sources, the use of transmission electron microscopes is no more limited to imaging or chemical analysis but has rather been extended to nanoengineering. This includes the e-beam induced growth, etching and structural transformation of nanomaterials. In this review we summarize recent progress on the e-beam induced morphological transformation of nanostructures from solid to hollow. We provide a detailed account of the processes reported so far in the literature with a special emphasis on the mechanistic understanding of the e-beam induced hollowing of nanomaterials. Through an important number of examples, we discuss how one can achieve a precise control of such hollowing processes by understanding the fundamental mechanisms occurring at the atomic scale during the irradiation of solid nanostructures. Finally, we conclude with remarks and our own view on the prospective future directions of this research field.