  We present a detailed study of the dielectric response of ZnO using a
combination of low-loss momentum-resolved electron energy-loss spectroscopy
(EELS) and first-principles calculations at several levels of theory, from the
independent particle and the random phase approximation with different variants
of density functional theory (DFT), including hybrid and DFT$+U$ schemes; to
the Bethe-Salpeter equation (BSE). We use a method based on the $f$-sum rule to
obtain the momentum-resolved experimental loss function and absorption spectra
from EELS measurements. We characterize the main features in the direct and
inverse dielectric functions of ZnO and their dispersion, associating them to
single-particle features in the electronic band structure, while highlighting
the important role of many-body effects such as plasmons and excitons. We
discuss different signatures of the high anisotropy in the response function of
ZnO, including the symmetry of the excitonic wave-functions.
