High-energy gravitational scattering provides a remarkably simple window into the nonlinear dynamics of general relativity in the most extreme regime. In the Regge limit, where the center-of-mass energy is much larger than the momentum transfer, the interaction admits a natural description in terms of gravitational shock waves.  I will first review the exponentiation of the S-matrix in impact-parameter space and I will show how multi-Regge factorization reorganizes gravitational amplitudes into impact factors, Lipatov currents and transverse propagators, giving a perturbative description of shock-wave dynamics. In particular, I will discuss the emergence of the H diagram and its higher multi-H generalizations, and explain the distinction between quantum-suppressed BFKL-type evolution and genuinely classical leading-log contributions. Finally, I will comment on how this ultra-relativistic scattering picture extends beyond flat space, from boundary correlators in AdS to cosmological correlators in dS.