With the rapid development of radioactive-ion-beam facilities worldwide, many exotic nuclear phenomena have been observed or predicted in nuclei far from the β-stability line or close to the neutron (proton) drip lines, such as halos in atomic nuclei and shape decoupling in deformed halo nuclei. The study of exotic nuclear phenomena, including halos, is at the frontier of current nuclear physics research. The covariant density functional theory (CDFT) is one of the most successful models in nuclear physics. The CDFT has been widely used to study structures and properties of exotic nuclei. The deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has been developed and achieved a self-consistent description of deformed halo nuclei by including deformation and continuum effects, with the deformed relativistic Hartree-Bogoliubov equations solved in the Dirac Woods-Saxon basis. The DRHBc theory has been used to predict the deformed halo structure in ⁴⁴Mg and the shape decoupling between the core and halo. The theory has also been used to address unresolved problems concerning the radius and configuration of valence neutrons in ²²C, deformed halos in carbon and boron isotopes, particles in the classically forbidden regions in magnesium isotopes, and other similar phenomena. The rotational excitation of deformed halos has been investigated by implementing an angular momentum projection based on the DRHBc theory. This investigation has shown that the effects of deformed halos and shape decoupling are also present in the low-lying rotational excitation states of deformed halo nuclei.