  Compact object binaries formed from dynamics interactions will generically
have non-zero orbital eccentricity. The gravitational waves from such binaries
can change drastically depending on how large the eccentricity is, ranging from
emitted in small a subset of orbital harmonics at low eccentricities, to being
concentrated into intense bursts of radiation from each pericenter passage at
large eccentricities. Gravitational waves from such highly eccentric binaries
present themselves an intriguing systems for probing fundamental physics, but
also present interesting challenges in terms of detection. The presence of
orbital eccentricity in the gravitational wave signature gives an unequivocal
method of determining the origin of the binary, while the highly dynamical
nature of pericenter passage often enhances the physics associated with matter
and gravity. The generation of faithful models of the repeated burst signals
has proven challenging, and often sub-optimal detection strategies like power
stacking are considered for detection. This chapter reviews our current
understanding of eccentric binaries, the leading efforts to model their
gravitational wave emission, and the physics that can be probed with these
detections.
