Describe the current state of quantum gravitational research.

Quantum gravity is the study of theories which incorporate known
gravitational and quantum phenomena. This usually involves the
assumption that gravity is itself a quantum phenomenon.

( http://www.maths.nott.ac.uk/personal/jwb/qg.html )

Quantam physicists are working towards a grand unified theory, to
unite the four fundamental forces. These are electromagnetism,
gravity, weak nuclear force, and strong nuclear force.  Quantum Field
Theory, or QFT currently is able to bring together three out of four
of these forces. Gravity is the one force that doesn't fit into the
Quantum Field Theory.

When one tries to apply the ideas of the Quantum Field Theory to
General Relativity, the results aren't physically possible. For
example, the forces between two gravitons (particles which are to
gravity what photons are to light) becomes infinite. Currently, a way
to combine Einstein's General Relativity theory and the QFT is what's
being sought.

The M-Theory is an attempt to combine all of the other theories which
attempt to describe everything. Unlike the QFT, the M-Theory is made
up of theories which describe everything as strings which vibrate in
certain ways, and forces are a result of this as well.

( http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html )

Quantum Gravity isn't a simple subject, but I have tried to simplify
it a bit here.

Additional Resources:

http://directory.google.com/Top/Science/Physics/Quantum_Mechanics/Quantum_Field_Theory/Gravitation/

http://directory.google.com/Top/Science/Physics/Quantum_Mechanics/Quantum_Field_Theory/

http://directory.google.com/Top/Science/Physics/Quantum_Mechanics/Quantum_Field_Theory/Superstrings/

http://directory.google.com/Top/Science/Physics/Relativity/

Search Strategy: Search for "gravity" and "quantum mechanics" on
directory.google.com

--
Sam Kennedy

There is no widely accepted quantum theory of gravity. String theories
with supersymmetry might provide a basis for quantum theory of
gravity. There are different string theories, like the original string
theory, Bosonic String Theory, superstring theories and heterotic
string theories. Superstring theories are different aspects of
M-theory.

http://www.jupiterscientific.org/sciinfo/gravity.html
http://www.newton.cam.ac.uk/programs/MTH/
http://www.damtp.cam.ac.uk/user/gr/public/qg_ss.html

I posted this answer with a short comment at:
http://www.bjklein.com/forum/topic.asp?TOPIC_ID=531&ARCHIVE=&whichpage=3

busybody-ga

Gravity is an artifact of curved space and motion.  A slight
confusion, space is said to be curved when it is more accurate to say
space is the curve.  There is also motion within this curve by all
matter.  All particles of all matter are spinning in all dimensions. 
Mass objects, like a planet or proton, cause an increase in the rate
of curvature in that area of space due to their mass.  Likewise those
objects are moving through curved space.  Spinning objects moving in a
curve cause gyroscopic procession toward the center of the arc of
curvature.  In humans case, this would be the force felt as our body
weight toward the center of our planet earth.  Therefore gravity,
though unavoidable, is nothing more than an artifact of motion and
spinning particles experiencing gyroscopic procession.  I have built
apparatus to verify my theory and it all checks out as this model
predicts, therefore I believe this to be the correct model.  This is
original research by me and represents the first writing of my
findings.