Conceptual Problems in Quantum Gravity and Quantum Cosmology
  The search for a consistent and empirically established quantum theory of gravity is among the biggest open problems of fundamental physics. The obstacles are of formal and of conceptual nature. Here, I address the main conceptual problems, discuss their present status and outline further directions of research. For this purpose, the main current approaches to quantum gravity are briefly reviewed and compared. 
Claus Kiefer
gr-qc hep-th quant-ph