  The intrinsic nuclear shapes deviating from a sphere not only manifest
themselves in nuclear collective states but also play important roles in
determining nuclear potential energy surfaces (PES's) and fission barriers. In
order to describe microscopically and self-consistently nuclear shapes and
PES's with as many shape degrees of freedom as possible included, we developed
multidimensionally-constrained covariant density functional theories
(MDC-CDFTs). In MDC-CDFTs, the axial symmetry and the reflection symmetry are
both broken and all deformations characterized by $\beta_{\lambda\mu}$ with
even $\mu$ are considered. We have used the MDC-CDFTs to study PES's and
fission barriers of actinides, the non-axial octupole $Y_{32}$ correlations in
$N = 150$ isotones and shapes of hypernuclei. In this Review we will give
briefly the formalism of MDC-CDFTs and present the applications to normal
nuclei.
