  We study in detail sub-GeV dark matter scattering off electrons in xenon,
including the expected electron recoil spectra and annual modulation spectra.
We derive improved constraints using low-energy XENON10 and XENON100
ionization-only data. For XENON10, in addition to including electron-recoil
data corresponding to about $1-3$ electrons, we include for the first time
events with $\gtrsim 4$ electrons. Assuming the scattering is momentum
independent, this strengthens a previous cross-section bound by almost an order
of magnitude for dark matter masses above 50 MeV. The available XENON100 data
corresponds to events with $\gtrsim 4$ electrons, and leads to a constraint
that is comparable to the XENON10 bound above 50 MeV. We demonstrate that a
search for an annual modulation signal in upcoming xenon experiments (XENON1T,
XENONnT, LZ) could substantially improve the above bounds even in the presence
of large backgrounds. We also emphasize that in simple benchmark models of
sub-GeV dark matter, the dark matter-electron scattering rate can be as high as
one event every ten (two) seconds in the XENON1T (XENONnT or LZ) experiments,
without being in conflict with any other known experimental bounds. While there
are several sources of backgrounds that can produce single- or few-electron
events, a large event rate can be consistent with a dark matter signal and
should not be simply written off as purely a detector curiosity. This fact
motivates a detailed analysis of the ionization-only ("S2-only") data, taking
into account the expected annual modulation spectrum of the signal rate, as
well as the DM-induced electron-recoil spectra, which are another powerful
discriminant between signal and background.
