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 β λµ with even µ, such as β 20 , β 22 , β 30 , β 32 , β 40 , 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

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... ght actinides, shapes and potential energy surfaces of superheavy nuclei, octupole correlations between multiple chiral doublet bands in 78 Br, octupole correlations in Ba isotopes, the Y 32 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.