In this short review we present our recent results concerning the rotation of
atomic Bose-Einstein condensates confined in quadratic or quartic potentials,
and give an overview of the field. We first describe the procedure used to set
an atomic gas in rotation and briefly discuss the physics of condensates
containing a single vortex line. We then address the regime of fast rotation in
harmonic traps, where the rotation frequency is close to the trapping
frequency. In this limit the Landau Level formalism is well suited to describe
the system. The problem of the condensation temperature of a fast rotating gas
is discussed, as well as the equilibrium shape of the cloud and the structure
of the vortex lattice. Finally we review results obtained with a quadratic +
quartic potential, which allows to study a regime where the rotation frequency
is equal to or larger than the harmonic trapping frequency.Comment: Laser Physics Letters 2, 275 (2005