Highest-precision radial velocities are needed both to find Earth-like exoplanets and to follow the expansion of the Universe. While the required instrumentation is becoming available, limitations are now set by the physics of spectral-line formation. Dynamical motions in stellar atmospheres cause spectral lines to become asymmetric and their wavelengths to “flicker”. 3-D hydrodynamic models reveal patterns of wavelength displacements across stellar disks and such models can now be tested also for stars other than the Sun, exploiting exoplanet transits. Differential spectroscopy between various transit phases provide spectra of small stellar surface segments temporarily hidden behind the planet.   Ongoing exoplanet surveys are likely to find additional suitable host stars for spatially resolved stellar spectroscopy, identifying routes toward finding “true” Earth analogs.