  Collisionless shocks are loosely defined as shocks where the transition
between pre-and post-shock states happens on a length scale much shorter than
the collisional mean free path. In the absence of collision to enforce thermal
equilibrium post-shock, electrons and ions need not have the same temperatures.
While the acceleration of electrons for injection into shock acceleration
processes to produce cosmic rays has received considerable attention, the
related problem of the shock heating of quasi-thermal electrons has been
relatively neglected. In this paper we review that state of our knowledge of
electron heating in astrophysical shocks, mainly associated with supernova
remnants (SNRs), shocks in the solar wind associated with the terrestrial and
Saturnian bowshocks, and galaxy cluster shocks. The solar wind and SNR samples
indicate that the ratio of electron temperature to ion temperature declines
with increasing shock speed or Alfvenic Mach number. We discuss the extent to
which such behavior can be understood via cosmic ray-generated waves in a shock
precursor, which then subsequently damp by heating electrons. Finally, we
speculate that a similar mechanism may be at work for both solar wind and SNR
shocks.

Astrophysics of Galaxies;High Energy Astrophysical Phenomena