  We study the eikonal scattering of two gravitationally interacting bodies, in
the regime of large angular momentum and large center of mass energy. We show
that eikonal exponentiation of the scattering phase matrix is a direct
consequence of the group contraction $SU(2)\to ISO(2)$, from rotations to the
isometries of the plane, in the large angular momentum limit. We extend it to
all orders in the scattering angle, and for all masses and spins. The emergence
of the classical limit is understood in terms of the continuous-spin
representations admitted by $ISO(2)$. We further investigate the competing
classical vs quantum corrections to the leading classical eikonal scattering,
and find several interesting examples where quantum corrections are more
important than Post-Minkowskian's. As a case of study, we analyse the
scattering of a photon off a massless neutral scalar field, up to
next-to-leading order in the Newton constant, and to leading order in the fine
structure constant. We investigate the causal structure of the eikonal regime
and establish an infinite set of non-linear positivity bounds, of which
positivity of time delay is the simplest.
