The methods that are actively used for electronic structure calculations of low-lying states of heavy- and superheavy-element compounds are briefly described. The advantages and disadvantages of the Dirac-Coulomb-Breit Hamiltonian, Huzinaga-type potential, shape-consistent Relativistic Effective Core Potential (RECP), and Generalized RECP are discussed. The nonvariational technique of the electron-structure restoration in atomic cores after the RECP calculation of a molecule is presented. The features of the approaches accounting for electron correlation, the configuration interaction and coupled cluster methods, are also described. The results of calculations on E113, E114, U, and other heavy-atom systems are presented.