(2.1.31) Schwerdtfeger : We should be reminded that the charge density ρ(r,t) is not Lorentz invariant. As relativistic quantum (field) theory demands a fully covariant formalism, we have to use the four-current density j µ as a function of the four-position x µ instead of the charge density, the latter appearing only as the time-like (first) component of the four-vector (ρ, j x /c, j y /c, j z /c), where c is the speed of light in vacuum. The Hohenberg-Kohn theorem has been generalized to the relativistic domain by Rajagopal and Callaway 57 and field-theoretical aspects have also been taken into account by Engel . Beside this enormous progress on the theoretical side, it is fair to say that applications in this most rigorous relativistic framework using the current-dependent exchange-correlation energy functional are more or less absent. The main reason lies, as one can guess, in the fact that relativistic DFT (RDFT) faces exactly the same fundamental problems as DFT in the nonrelativistic domain. As we know, relativistic effects can be very large for electronic properties of compounds containing heavy elements, often larger than the error introduced by many DFAs, thus justifying the introduction of the exchange-correlation functional into the (no-pair) Dirac-Coulomb (DC) equation (the Douglas-Kroll Kohn-Sham scheme) or into its corresponding two-component (such as exact two-component [X2C]) or scalar relativistic schemes, with or without the relativistic pseudopotential approximation. The latter together with DFT is clearly the main workhorse in solid-state physics. One may however, question the inclusion of smaller radiative QED corrections into RDFT as it cannot compete with more accurate wave-function based methods. On the other hand, we should mention that RDFT approximations based on the density ρ and the (noncollinear) magnetization density m have now become feasible and useful in many applications.