Non-perturbative quantum gravity

The author presents a summary of the current status of a program whose aim is to carry out an exact canonical quantization of gravity. It is well-known that attempts to apply perturbative, field theoretic techniques to obtain a quantum version of general relativity fail by their own criteria. Introduction of higher derivative terms and extension to supergravity have not improved this situation. The problem, it would seem, lies in the basic assumption of perturbative methods that space-time can be approximated by a smooth manifold well below the Planck scale, where, as simple physical arguments indicate, quantum gravity effects should in fact be very strong. This view is also supported by the recent results on the failure of the perturbative string theory