Relativistic quantum chemical ab initio methods for calculations of the electronic structures of actinide and transactinide atoms and molecules are briefly reviewed. The importance of relativistic and electron correlation effects for heavy-element quantum chemical investigations is emphasized. In addition, the need to go beyond the Dirac one-electron relativity and to include, for example, the Breit interaction for the relativistic two-electron interaction or even low-order contributions from quantum electrodynamics is shown for specific examples. The possible entries on the three axes of the coordinate system of ab initio quantum chemical calculations—Hamiltonian axis, one-, and many-particle basis set axes—are summarized. Several choices for relativistic Hamiltonians at the all-electron and valence-only level are introduced and compared, and the principal strategies to account for relativistic effects, including spin–orbit interaction and electron correlation effects in calculations, are discussed. Some remarks on problems when applying density functional theory to actinide and transactinide systems are made. Finally, a few selected examples show the range of applicability of the currently available methods for theoretical investigations of the heaviest known elements and their chemistry.