  The capture and subsequent in--spiral of compact stellar remnants by central
massive black holes, is one of the more interesting likely sources of
gravitational radiation detectable by LISA. The relevant stellar population
includes stellar mass black holes, and possibly intermediate mass black holes,
generally on initially eccentric orbits. Predicted detectable rates of capture
are highly uncertain, but may be high enough that source confusion is an issue.
Foreground events with relatively high signal-to-noise ratio may provide
important tests of general relativity. I review the rate estimates in the
literature, and the apparent discrepancy between different authors' estimates,
and discuss some of the relevant uncertainties and physical processes. The
white dwarf mergers rate are uncertain by a factor of few; the neutron star
merger rate is completely uncertain and likely to be small; the black hole
merger rate is likely to be dominant for detectable mergers and is uncertain by
at least two orders of magnitude, largely due to unknown physical conditions
and processes. The primary difference in rate estimates is due to different
initial conditions and less directly due to different estimates of key physical
processes, assumed in different model scenarios for in-spiral and capture.
