Phase composition and nanostructure of layered and irregular massive impact diamond grains from the Popigai astrobleme have been investigated by Raman spectroscopy and high-resolution electron microscopy and the conditions of phase transformations are discussed. Several coexisting carbon phases forming tight aggregates have been found, including cubic and hexagonal diamond polymorphs, graphite, amorphous carbon, fullerene-like/onion-like carbon. The latter is described within impact diamonds for the first time. It is proposed that the formation of onion-like carbon, in both layered and massive impact diamond grains, is connected with high-pressure graphite transformation or post-pressure stress cooling which causes the partial back transformation of diamond nanocrystallites to sp2 carbon. However, a possible relict origin of the fullerene-like carbon from the impacted initial sedimentary rocks with fullerenes and fullerene-like substances, like shungite or coal, can not be excluded. The difference between micro- and nanostructures of layered and irregular massive impact grains is presented.