Particle loss due to the emission of single energetic beamstrahlung photons in beam collisions is shown to impose a fundamental limit on storage-ring luminosities at energies greater than 2E~140 GeV for head-on collisions and 2E~40 GeV for crab-waist collisions. Above these threshold energies, the suppression factor due to beamstrahlung scales as 1/E^{4/3}, and for a fixed power of synchrotron radiation, the luminosity L is proportional to R/E^{13/3}, where R is the collider radius. For 2E > 150 GeV, both collision schemes have similar luminosity limits. The luminosities attainable at storage-ring and linear-collider (LC) 2E=240 GeV Higgs factories are comparable; at higher energies, LCs are preferable. This conference paper is based on my recent PRL publication [1], supplemented with additional comments on linac-ring e+e- colliders and ring e+e- colliders with charge compensation (four-beam collisions).
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