The generalized relativistic effective core potentials (GRECPs) for calculations of electronic structure and physical-chemical properties of compounds containing superheavy elements (Z ≥ 104) are presented. Features of accounting for the finite nuclear size effects which are unusually large for superheavy elements are discussed in details. Accuracy of the GRECPs is analyzed in atomic calculations compared to allelectron studies with the Dirac-Coulomb-Breit Hamiltonian. Applications of the GRECP method in molecular and cluster calculations are surveyed. K E Y W O R D S relativistic effective core potentials, pseudopotentials, superheavy elements, finite nuclear size