  Excitations of chiral rotation observed in triaxial nuclei and magnetic
and/or antimagnetic rotations seen in near-spherical nuclei have attracted a
lot of attention. Unlike conventional rotation in well-deformed or
superdeformed nuclei, here the rotational axis is not necessary coinciding with
any principal axis of the nuclear density distribution. Thus, tilted axis
cranking is mandatory to describe these excitations self-consistently in the
framework of covariant density functional theory (CDFT). We will briefly
introduce the formalism of tilted axis cranking CDFT and its application for
magnetic and antimagnetic rotation phenomena. Configuration-fixed CDFT and its
predictions for nuclear chiral configurations and for favorable triaxial
deformation parameters are also presented, and the discoveries of the multiple
chiral doublets (M\c{hi}D) in 133Ce and 103Rh are discussed.
