The current status of theoretical understanding of the optical and magneto-
optical (MO) spectra of 3d, 4f and 5f compounds is reviewed. Energy band th
eory based upon the local spin-density approximation (LSDA) describes the o
ptical and MO spectra of transition metal compounds reasonably well. Exampl
es which we examine in detail are XPt3 compounds (with X=3d V, Cr, Mn, Fe,
and Co) in the AuCu3 structure, ternary Heusler alloys NiMnSb, PdMnSb, PtMn
Sb, and MnBi compound. The LSDA, which is capable of describing the spectra
of transition-metal alloys with high accuracy, does not suffice for lantha
nide compounds having a correlated 4f shell. A satisfactory description of
the optical spectra could be obtained by using a generalization of the LSDA
, in which explicitly f electron Coulomb correlations are taken into accoun
t (LSDA+U approach). As examples of this group we consider CeSb and CeBi. F
or CeSb a record Kerr angle of 90 degrees was very recently reported, 90 de
grees is the absolute maximum value that can be measured. It is two orders
of magnitude larger than the values that are commonly measured for transiti
on-metal compounds, and about one order of magnitude larger than values max
imally achieved for other lanthanide and actinide compounds. A third group
consist of uranium 5f compounds. In those compounds where the 5f electrons
are rather delocalized, the LSDA describes the MO spectra reasonably well.
As examples of this group we consider UAsSe and URhAl. Particular difficult
ies occur for the uranium compounds where the 5f electrons are neither delo
calized nor localized, but more or less semilocalized. Typical examples are
US, USe and UTe. The semilocalized 5f's are, however, not inert, but their
interaction with conduction electrons plays an important role. Recently ac
hieved improvements for describing such compounds are discussed. (C) 1999 A
merican Institute of Physics. [S1063-777X(99)00106-1].