  The calculation of electronic properties of materials is an important task of
solid state theory, albeit particularly difficult if electronic correlations
are strong, for example in transition metals, their oxides and in f-electron
systems. The standard approach to material calculations, the density functional
theory in its local density approximation (LDA), incorporates electronic
correlations only very rudimentarily and fails if the correlations are strong.
Encouraged by the success of dynamical mean field theory (DMFT) in dealing with
strongly correlated model Hamiltonians, physicists from the bandstructure and
the many-body community have joined forces and developed a combined LDA+DMFT
method recently. Depending on the strength of electronic correlations, this new
approach yields a weakly correlated metal as in LDA, a strongly correlated
metal, or a Mott insulator. By now, this approach is widely regarded as a
breakthrough for electronic structure calculations of strongly correlated
materials.
  The author will review this LDA+DMFT method and also discuss alternative
approaches to employ DMFT in electronic structure calculations, for example, by
replacing the LDA part by the so-called GW approximation. Different methods to
solve the DMFT equations are introduced with a focus on those that are suitable
for realistic calculations with many orbitals. An overview of the successful
application of LDA+DMFT to a wide variety of materials, ranging from Pu and Ce,
to Fe and Ni, to numerous transition metal oxides, is given.
