In dense stellar regions like globular clusters, black
hole-neutron star and neutron star-neutron star binaries may form dynamically
and merge with significant orbital eccentricities. These mergers are not
only a potential gravitational wave source for upcoming detectors like Advanced
LIGO, but could also give rise to a number of electromagnetic transients
including short gamma-ray bursts. In this talk I will present results
from general-relativistic, hydrodynamic simulations of black hole-neutron star
and binary neutron star mergers and discuss the large variability with impact
parameter that these systems exhibit in dynamics and outcome. I will also
discuss ongoing work to model the gravitational wave signals from these events
and assess the prospects for detection.