I’ll give a critical review (from a personal viewpoint) of the present status and recent progress of loop and spin foam approaches to quantization of four-dimensional general relativity. I’ll argue that none of these approaches provided up to now a model, which can be considered as a candidate for a theory of quantum gravity. In particular, loop quantum gravity is likely to be an anomalous theory, whereas the present spin foam models suffer from incomplete (or even wrong) implementation of constraints of general relativity.

LPTA, Université de Montpellier