The current status of relativistic density functional theory is reviewed. For most applications relevant to chemistry, relativistic corrections to the electron interaction and radiative corrections are not important, and the Ž . four-component Dirac᎐Kohn᎐Sham model can be viewed as a reference. More Ž . approximate two-component schemes are much more popular not only because of the lower computational effort, but also because, in chemistry, one is only interested in the electronic states of a system, and the two-component methods in one way or another project out the positronic states. It is even possible to arrive at one-component relativistic methods if one can neglect spin-orbit coupling, which is often done for closed-shell compounds containing heavy atoms. Various such schemes are available today, based on first-order perturbation theory or even including higher order corrections, based on the Douglas᎐Kroll᎐Hess transformation, or on the so-called regular approximation. In recent years, analytical geometry gradients have been implemented for all Ž . these methods, the gradient for the zeroth-order regular approximation ZORA being presented in this work for the first time. The availability of such geometry gradients is quite important for the applicability of these methods to ''real chemistry''; that is, polyatomic molecules. Results of relativistic density functional methods are collected for some benchmark molecules. Then some results for various tungsten pentacarbonyl phosphines, platinum tricarbonyl phosphines, and molybdenum dinitrogen phosphine carbonyls, as obtained with first-order relativistic density functional calculations by means of direct Ž . perturbation theory DPT , are presented. In another application, the force field of molybdenum, tungsten, and uranium hexafluoride in the metal᎐fluorine stretch region is calculated at both the DPT and ZORA levels. First-order relativistic calculations are reasonable for second-and third-row transition metal Ž . compounds mainly 4d and 5d electrons involved in bonding , whereas, for Ž . uranium and gold compounds mainly 5f, 6d, and 6s electrons involved , higher order relativistic corrections must be considered.