  We study gravitational shock waves using scattering amplitude techniques.
After first reviewing the derivation in General Relativity as an
ultrarelativistic boost of a Schwarzschild solution, we provide an alternative
derivation by exploiting a novel relation between scattering amplitudes and
solutions to Einstein's field equations. We prove that gravitational shock
waves arise from the classical part of a three point function with two massless
scalars and a graviton. The region where radiation is localized has a
distributional profile and it is now recovered in a natural way, thus bypassing
the introduction of singular coordinate transformations as used in General
Relativity. The computation is easily generalized to arbitrary dimensions and
we show how the exactness of the classical solution follows from the absence of
classical contributions at higher loops. A classical double copy between
gravitational and electromagnetic shock waves is also provided and for a
spinning source, using the exponential form of three point amplitudes, we infer
a remarkable relation between gravitational shock waves and spinning ones, also
known as gyratons. Using this property, we infer a family of exact solutions
describing gravitational shock waves with spin. We then compute the phase shift
of a particle in a background of shock waves finding agreement with an earlier
computation by Amati, Ciafaloni and Veneziano for particles in the high energy
limit. Applied to a gyraton, it provides a result for the scattering angle to
all orders in spin.
