According to general relativity, the remnant of a binary black hole merger is a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of damped exponentials (“quasinormal modes”), with frequencies and damping times that depend only on the mass and spin of the remnant. The observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes, just like the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on: (1) the role of nonlinearities in ringdown modeling, (2) the current observational status of black hole spectroscopy, and (3) future prospects for the observability of modified gravity effects and nonlinear modes.