The discovery of gravitational waves from merging black holes marked the beginning of a new way of exploring the Universe. I will start by describing this breakthrough. Planned next-generation gravitational-wave observatories will dramatically extend our reach, enabling the detection of gravitational-wave signals from deep into the early cosmic history. The leap in experimental sensitivity demands a corresponding advance in theoretical precision. I will outline the main theoretical approaches underlying highly accurate waveform predictions, which are essential for interpreting these observations. In the context of one of the standard approaches, I will explain how powerful theoretical methods in quantum field theory, used to understand elementary-particle collisions, are being used to obtain state-of-the-art predictions of gravitational-wave emission in Einstein’s theory. Finally, I will explain how this approach reveals a deep and unexpected unity between gravity and the other known forces.