  We first present a review, intended for classical relativists, of the
ultraviolet difficulties faced by local quantum gravity theories in both the
usual Einstein versions and in their supergravity extensions, at least
perturbatively. These problems, present in arbitrary dimensions, are traceable
to the dimensionality of the Einstein constant. We then summarize very recent
results about supergravity at the highest allowed dimension, D=11, showing that
also this unique model suffers from infinities already at 2 loops, despite its
high degree of supersymmetry. The conclusion is that there is no viable
nonghost quantum field model that includes general relativity.
