  The use of effective local Coulomb interactions that are dynamical, that is,
frequency-dependent, is an efficient tool to describe the effect of long-range
Coulomb interactions and screening thereof in solids. The dynamical character
of the interaction introduces the coupling to screening degrees of freedom such
as plasmons or particle-hole excitations into the many-body description. We
summarize recent progress using these concepts, putting emphasis on dynamical
mean field theory (DMFT) calculations with dynamical interactions ("doubly
dynamical mean field theory"). We discuss the relation to the combined GW+DMFT
method and its simplified version "Screened Exchange DMFT", as well as the
cumulant schemes of many-body perturbation theory. On the example of the simple
transition metal SrVO3, we illustrate the mechanism of the appearance of
plasmonic satellite structures in the spectral properties, and discuss
implications for the low-energy electronic structure.
