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The new generation of spectrometers designed for extreme precision radial velocities enable correspondingly precise stellar spectroscopy. It is now fruitful to theoretically explore what the information content would be if stellar spectra could be studied with spectral resolutions of a million or more, and to deduce what signatures remain at lower resolutions. Hydrodynamic models of stellar photospheres predict how line profiles shapes, asymmetries, and convective wavelength shifts vary from disk center to limb. Corresponding high-resolution spectroscopy across spatially resolved stellar disks is now practical using differential observations during exoplanet transits, thus enabling the testing of such models. A most demanding task is to understand and to model spectral microvariability toward the radial-velocity detection of also low-mass planets in Earth-like orbits around solar-type stars. Observations of the Sun-as-a-star with extreme precision spectrometers now permit searches for spectral-line modulations on the level of a part in a thousand or less, feasible to test against hydrodynamic models of various solar features.