  Accurate analysis of precision ranges to the Moon has provided several tests
of gravitational theory including the Equivalence Principle, geodetic
precession, parameterized post-Newtonian (PPN) parameters $\gamma$ and $\beta$,
and the constancy of the gravitational constant {\it G}. Since the beginning of
the experiment in 1969, the uncertainties of these tests have decreased
considerably as data accuracies have improved and data time span has
lengthened. We are exploring the modeling improvements necessary to proceed
from cm to mm range accuracies enabled by the new Apache Point Observatory
Lunar Laser-ranging Operation (APOLLO) currently under development in New
Mexico. This facility will be able to make a significant contribution to the
solar system tests of fundamental and gravitational physics. In particular, the
Weak and Strong Equivalence Principle tests would have a sensitivity
approaching 10$^{-14}$, yielding sensitivity for the SEP violation parameter
$\eta$ of $\sim 3\times 10^{-5}$, $v^2/c^2$ general relativistic effects would
be tested to better than 0.1%, and measurements of the relative change in the
gravitational constant, $\dot{G}/G$, would be $\sim0.1$% the inverse age of the
universe. Having this expected accuracy in mind, we discusses the current
techniques, methods and existing physical models used to process the LLR data.
We also identify the challenges for modeling and data analysis that the LLR
community faces today in order to take full advantage of the new APOLLO ranging
station.
