We review our quantum chemical molecular dynamics (QM/MD)-based studies of carbon nanostructure formation under nonequilibrium conditions that were conducted over the past 10C years. Fullerene, carbon nanotube, and graphene formation were simulated on the nanosecond time scale, considering experimental conditions as closely as possible. An approximate density functional method was employed to compute energies and gradients on the fly in direct MD simulations, while the simulated systems were pushed away from equilibrium via carbon concentration or temperature gradients. We find that carbon nanostructure formation from feedstock particles involves a phase transition of sp to sp 2 carbon phases, which begins with the formation of Y-junctions, followed by a nucleus consisting of pentagons, hexagons, and heptagons. The dominance of hexagons in the synthesized