Gravitational waves—ripples of warped spacetime—are an entirely new spectrum for observing the universe. The Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo observatory have ignited the era of gravitational-wave astronomy, observing dozens of collisions of black holes and neutron stars  to date. Interpreting these observations without bias requires accurate models of the expected waves, models only possible with numerical relativity—solving Einstein's equations on supercomputers. In this talk, I will highlight progress and challenges in using numerical relativity to model binary black holes and the gravitational waves they emit, particularly the challenge of simulating merging binary black holes with spins that are nearly extremal (that is, near the theoretical maximum). I will also discuss how a new generation of observatories, planned for the next decade, will be so much more sensitive that they will need a new generation of numerical relativity calculations with far higher accuracy than today's state of the art. I will present recent progress toward enabling SpECTRE, an open-source, next-generation numerical-relativity code, to simulate binary black holes with rapid spins.