  Detecting the end of the cosmic-ray (CR) electron spectrum would provide
important new insights. While we know that Milky Way sources can accelerate
electrons up to at least $\sim$1PeV, the observed CR electron spectrum at Earth
extends only up to 5TeV (possibly 20TeV), a large discrepancy. The question of
the end of the CR electron spectrum has received relatively little attention,
despite its importance. We take a comprehensive approach, showing that there
are multiple steps at which the observed CR electron spectrum could be cut off.
At the highest energies, the accelerators may not have sufficient luminosity,
or the sources may not allow sufficient escape, or propagation to Earth may not
be sufficiently effective, or present detectors may not have sufficient
sensitivity. For each step, we calculate a rough range of possibilities.
Although all of the inputs are uncertain, a clear vista of exciting
opportunities emerges. We outline strategies for progress based on CR electron
observations and auxiliary multi-messenger observations. In addition to
advancing our understanding of CRs in the Milky Way, progress will also sharpen
sensitivity to dark matter annihilation or decay.
