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Rotating nuclei: from ground state to the extremes of spin and deformation

The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties sensitively depend on time-odd mean fields and currents in density functional theories. Moreover, they show a considerable interplay of collective and single-particle degrees of freedom. In this chapter, I discuss the basic features of the description of rotating nuclei in one-dimensional cranking approximation of covariant density functional theory. The successes of this approach to the description of rotating nuclei at low spin in pairing regime and at high spin in unpaired regime in wide range of deformations (from normal to hyperdeformation) are illustrated. I also discuss the recent progress and open questions in our understanding of the role of proton-neutron pairing in rotating nuclei at $N\approx Z$, the physics of band termination and other phenomena in rotating nuclei.