 The difficulties in reconciling quantum theory and gravity into some form of quantum gravity come from the prima facie incompatibility of general relativity, Einstein’s relativistic theory of gravitation, and quantum field theory, the framework for the description of the other three forces (electromagnetism and the strong and weak nuclear interactions). Whence the incompatibility? General relativity is described by Einstein’s equations, which amount to constraints on the curvature of spacetime (the Einstein tensor on the left-hand side) due to the presence of mass and other forms of energy, such as electromagnetic radiation (the stress-energy-momentum tensor on the right-hand side). (See John Baez’s webpages in  Other Internet Resources  for an excellent introduction.) In doing so, they manage to encompass traditional, Newtonian gravitational phenomena such as the mutual attraction of two or more massive objects, while also predicting new phenomena such as the bending and red-shifting of light by these objects (which have been observed) and the existence of gravitational radiation (until very recently, with the direct detection of gravitational waves by LIGO, this was, of course, only indirectly observed via the decrease in the period of binary pulsars-see the  1993 Physics Nobel Prize presentation speech by Carl Nordling.)