  We examine the ultraviolet behaviour of supergravity theories as a function
of dimension and number of supercharges. We do so by the computation of one and
two-loop physical on-shell four point amplitudes. For maximal supergravity, our
computations prove the non-renomalisability of supergravity for $D \geq 6$
(including the maximal D=11 case) and give strong evidence for the existance of
a five-loop counterterm in D=4. For type I supergravity our results indicate
similar patterns. e shall also explore a remarkable relationship between
gravity amplitudes and those of Yang-Mills theories. In many ways gravity
calculations discover features which relate to the equivalent Yang-Mills
features by a squaring proceedure.
