In recent years, we have developed the multidimensionally-constrained covariant density functional theories (MDC-CDFTs) in which both axial and spatial reflection symmetries are broken and all shape degrees of freedom described by /3k, with even it, such as /320, /322, /330, /332, /340, etc., are included self-consistently. The MDC-CDFTs have been applied to the investigation of potential energy surfaces and fission barriers of actinide nuclei, third minima in potential energy surfaces of light actinides, shapes and potential energy surfaces of superheavy nuclei, octupole correlations between multiple chiral doublet bands in 78Br, octupole correlations in Ba isotopes, the Y32 correlations in N = 150 isotones and Zr isotopes, the spontaneous fission of Fm isotopes, and shapes of hypernuclei. In this contribution we present the formalism of MDC-CDFTs and the application of these theories to the study of fission barriers and potential energy surfaces of actinide nuclei.