There’s a readable recent summary of progress in and results from lunar laser ranging in:
http://arxiv.org/pdf/1309.6294.pdf
The article begins with:
Since 1969, lunar laser ranging (LLR) has provided high-precision measurements of the
Earth-Moon distance, contributing to the foundations of our knowledge in gravitation
and planetary physics. While being the most evident force of nature, gravity is in fact the
weakest of the fundamental forces, and consequently the most poorly tested by modern
experiments. Einstein’s general relativity – currently our best description of gravity – is
fundamentally incompatible with quantum mechanics and is likely to be replaced by
a more complete theory in the future. A modi fied theory would, for example, predict
small deviations in the solar system that, if seen, could have profound consequences for
understanding the universe as a whole.
Utilizing reflectors placed on the lunar surface by American astronauts and Soviet
rovers, LLR measures the round-trip travel time of short pulses of laser light directed to
one reflector at a time (Fig. 1). By mapping the shape of the lunar orbit, LLR is able to
distinguish between competing theories of gravity. Range precision has improved from
a few decimeters initially to a few millimeters recently, constituting a relative precision
of 10^-9 to 10^-11. Leveraging the raw measurement across the Earth-Sun distance provides
another two orders of magnitude for gauging relativistic e ffects in the Earth-Moon-Sun
system.
As LLR precision has improved over time, the technique has remained at the cutting
edge of tests of gravitational phenomenology and probes of the lunar interior, and has
informed our knowledge of Earth orientation, precession, and coordinate systems. …