  The first part of this article centers on the fact that key features of the
dynamical response of weakly-correlated materials (the alkalis, Al), have been
found experimentally to differ qualitatively from simple-model behavior. In the
absence of ab initio theory, the surprises embodied in the experimental data
were imputed to effects of dynamical correlations. We summarize results of ab
initio investigations of linear response, performed within time-dependent
density-functional theory (TDDFT), in which the unexpected features of the
observed spectra are shown to be due to band-structure effects. Contrary to
conventional wisdom, the response cannot be understood "universally," in terms
of a simple scaling with the density, on going from metal to metal (e.g.,
through the alkali series) --even the shape of the dispersion curve for the
plasmon energy is system-specific. The second part of this article starts out
with the observation that a similar ab initio study of systems with more
complex electronic structures would require the availability of a realistic
approximation for the dynamical many-body kernel entering the density-response
function in TDDFT. Thus, we outline a diagrammatic alternative, framed within
the conserving-approximation method of Baym and Kadanoff. Using as a benchmark
the band gap of Si obtained in the GW approximation, together with a
diagrammatic (and conserving) solution of the ensuing Bethe-Salpeter equation,
we discuss issues involving conservation laws, self-consistency, and sum rules.
These conceptual issues are particularly important for the development of ab
initio methods for the study of dynamical response and quasiparticle band
structure of strongly-correlated materials. We argue that inclusion of
short-range correlations absent in the GW approximation is a must, even in Si.
