The eikonal exponentiation provides a natural strategy to calculate classical gravitational observables from the loop expansion of scattering amplitudes. Such observables include the deflection angle, the losses of energy and angular momentum, as well as the emitted wave-forms for encounters of compact objects. In this talk I will illustrate recent progress in this direction and discuss open challenges that lie ahead, concerning both the precision frontier and the inclusion of relevant additional effects beyond the point-particle limit. In particular, I will present intriguing phenomena that take place in the high-energy regime, as the colliding objects' velocities approach the speed of light.