  Many of the fascinating and unconventional properties of several
transition-metal compounds with partially filled d-shells are due to strong
electronic correlations. While local correlations are in principle treated
exactly within the frame of the dynamical mean-field theory, there are two
major and interlinked routes for important further methodical advances: On the
one hand, there is a strong need for methods being able to describe
material-specific aspects, i.e., methods combining the DMFT with modern
band-structure theory, and, on the other hand, nonlocal correlations beyond the
mean-field paradigm must be accounted for. Referring to several concrete
example systems, we argue why these two routes are worth pursuing and how they
can be combined, we describe several related methodical developments and
present respective results, and we discuss possible ways to overcome remaining
obstacles.
