Carbon is a surprising material in all respects. In this Review, we present results of metadynamics calculations for crystal structure prediction of novel carbon polymorphs with even and odd rings. So-called superhard graphite results from cold-compressing graphite. We review the results of molecular dynamics simulations on the graphite-to-diamond phase transition, that yields Oganov's M-carbon. The latter, like some of the modifications predicted by metadynamics, features five- and seven-membered odd rings. We identify the role of odd rings at times of phase nucleation, and we speculate on the preference for odd-membered rings over even motifs in a context of nucleation and phase growth.