Theories that seek to explain the outstanding puzzles of the Standard Model of particle physics often predict new, light, feebly-interacting particles whose discovery requires novel search strategies. These include light spin-0 axions and spin-1 dark photons. I will discuss how rotating black holes source clouds of exponentially large numbers of gravitationally-bound particles and so create nature's laboratories for ultralight bosons. This process causes black holes to spin down and the bound bosons emit gravitational waves, allowing observatories such as LIGO and Virgo to search for new particles. For a new dark photon particle that couples to the Standard Model, the systems could undergo dramatic electromagnetic cascades and appear as novel pulsar-like objects in the sky.