  The covariant density functional theory with a few number of parameters has
been widely used to describe the ground-state and excited-state properties for
the nuclei all over the nuclear chart. In order to describe exotic properties
of unstable nuclei, the contribution of the continuum and its coupling with
bound states should be treated properly. In this Topical Review, the
development of the covariant density functional theory in continuum will be
introduced, including the relativistic continuum Hartree-Bogoliubov theory, the
relativistic Hartree-Fock-Bogoliubov theory in continuum, and the deformed
relativistic Hartree-Bogoliubov theory in continuum. Then the descriptions and
predictions of the neutron halo phenomena in both spherical and deformed nuclei
will be reviewed. The diffuseness of the nuclear potentials, nuclear shapes and
density distributions, and the impact of the pairing correlations on nuclear
size will be discussed.
