  This is a review of Glauber's asymptotic diffraction theory, in which
diffractive scattering is described in terms of interference between
semiclassical amplitudes, resulting from a stationary-phase approximation.
Typically two such amplitudes are sufficient to accurately describe elastic
scattering, but the stationary points are located at complex values of the
impact parameter. Their separation controls the interference pattern, and their
offsets from the real axis determine the overall fall-off with momentum
transfer. Asymptotically, at large momentum transfers, the stationary points
move towards singularities of the profile function. I also include some
reminiscences from our collaboration.
