After recalling results(some of which going back as much as 35 years)on the eikonal approach to trasplanckian-energy collisions of light particles and strings, I will turn to recent applications of similar techniques to black-hole encounters and to theensuinggravitational radiation. I will particularly emphasize a few puzzles that have arisen — and only partially disappeared — in both regimes. The talk aims at a non-specialized audience.