Abstract: With the development of radioactive-ion-beam facilities, many exotic phenomena have been discovered or predicted in the nuclei far from the \beta stability line, including cluster structure, shell structure, deformed halo, and shape decoupling effects. The study of exotic nuclear phenomena is at the frontier of nuclear physics nowadays. The covariant density functional theory (CDFT) is one of the most successful microscopic models in describing the structure of nuclei in almost the whole nuclear chart. Within the framework of CDFT, toward a proper treatment of deformation and weak binding, the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) has been developed. In this contribution, we review the applications and extensions of the DRHBc theory to the study of exotic nuclei. The DRHBc theory has been used to investigate the deformed halos in B, C, Ne, Na, and Mg isotopes and the theoretical descriptions are reasonably consistent with available data. A DRHBc Mass Table Collaboration has been founded, aiming at a high precision nuclear mass table with deformation and continuum effects included, which is underway. By implementing the angular momentum projection based on the DRHBc theory, the rotational excitations of deformed halos have been investigated and it is shown that the deformed halos and shape decoupling effects also exist in the low-lying rotational excitation states of deformed halo nuclei.