Abstract Hercules X-1 is a nearly edge-on accreting X-ray pulsar with a warped accretion disk, precessing with a period of about 35 days. The disk precession allows for unique and changing sightlines toward the X-ray source. To investigate the accretion flow at a variety of sightlines, we obtained a large observational campaign on Her X-1 with XMM-Newton (380 ks exposure) and Chandra (50 ks exposure) for a significant fraction of a single disk precession cycle, resulting in one of the best data sets taken to date on a neutron star X-ray binary. Here we present the spectral analysis of the high state high-resolution grating and CCD data sets, including the extensive archival data available for this famous system. The observations reveal a complex Fe K region structure, with three emission line components of different velocity widths. Similarly, the high-resolution soft X-ray spectra reveal a number of emission lines of various widths. We correct for the uncertain gain of the European Photon Imaging Camera pn Timing mode spectra, and track the evolution of these spectral components with Her X-1 precession phase and observed luminosity. We find evidence for three groups of emission lines, the first of which originates in the outer accretion disk (10⁵ R _G from the neutron star). The second line group plausibly originates at the boundary between the inner disk and the pulsar magnetosphere (10³ R _G). The last group is too broad to arise in the magnetically truncated disk and instead must originate very close to the neutron star surface, likely from X-ray reflection from the accretion curtain (∼10² R _G).