  Supermassive stars (SMSs), with masses $>10^5$ M$_\odot$, have been proposed
as the possible progenitors of the most extreme supermassive black holes
observed at redshifts $z>6-7$. In this scenario ('direct collapse'), a SMS
accretes at rates $>0.1$ M$_\odot$ yr$^{-1}$ until it collapses to a black hole
via the general-relativistic (GR) instability. Rotation plays a crucial role in
the formation of such supermassive black hole seeds. The centrifugal barrier
appears as particularly strong in this extreme case of star formation.
Moreover, rotation impacts sensitively the stability of SMSs against GR, as
well as the subsequent collapse. In particular, it might allow for
gravitational wave emission and ultra-long gamma-ray bursts at black hole
formation, which represents currently the main observational signatures
proposed in the literature for the existence of such objects. Here, I present
the latest models of SMSs accounting for accretion and rotation, and discuss
some of the open questions and future prospects in this research line.
