LQG - outlined well here
http://en.wikipedia.org/wiki/Loop_quantum_gravity and here
http://relativity.livingreviews.org/...es/lrr-1998-1/
Briefly it tries to propose a classical framework to understand gravity, or more correctly quantum gravity. To do this it imposes both time and space are quantised at the smallest level - Planck units. Doing this satisfies some frameworks it must be validated against, but it makes no predictions outside of the standard model - so it can't be validated or denied. Trying to do so is extremely challenging mathematically. Getting it to agree with several major validation points from other theories (must pass tests) requires you to set parameters a certain way (without these constants being derived from fundamental constraints) so to make it work is variable. The field it encompasses too is so broad there is an over-abundance of topic areas to try and study and resolve.
Too it assumes spacetime has a lower limit without explaining why - which is rather a dubious concept. To fully understand it - well it gets abstractly tough really fast, with field effects and very high order maths (very, very high order).