  The inspirals of ``small'' ($1 - 100 M_\odot$) compact bodies through highly
relativistic orbits of massive (several $\times 10^5 M_\odot -$ several $\times
10^6 M_\odot$) black holes are among the most anticipated sources for the LISA
gravitational-wave antenna. The measurement of these waves is expected to map
the spacetime of the larger body with high precision, allowing us to test in
detail the hypothesis that black hole candidates are described by the Kerr
metric of general relativity. In this article, we will briefly describe how
these sources can be used to perform such a test. These proposed measurements
are often described as ``testing relativity''. This description is at best
somewhat glib: Because -- at least to date -- all work related to these
measurements assumes general relativity as the theoretical framework in which
these tests are performed, the measurements cannot be said to ``test
relativity'' in a fundamental way. More accurately, they test the {\it nature
of massive compact bodies within general relativity}. A surprising result for
such a test could point to deviations from general relativity, and would
provide an experimentally motivated direction in which to pursue tests of
gravity theories beyond GR.
