I am aware that that the most researched approach is that of string theory. I have also heard about quantum loop gravity. What other approaches are there to unify gravity and QFT? Also, please include a brief description of that approach, and how it is different from the others.
This sounds like an essay question :-)
There are lots and lots of suggestions for quantum gravity, few of which have convinced many. I would start with the list in the Wkikipedia article on quantum gravity and follow the links from there.
My own favourite amongst the also-rans is Causal Dynamical Triangulation because it seems an interesting idea, though I think its chance of success is low.