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.
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