The detection of gravitational waves from black hole (BH) mergers provides an inroad toward probing the interior of astrophysical BH’s. The view in general relativity of the interior of a BH as a region of empty space except for a possibly singular core appears to be in contradiction with the laws of quantum mechanics and so cannot be correct. I will describe a simple method for answering the following question: Does the BH interior contain some distribution of matter or is it mostly empty? The proposal is premised on the idea that any BH-like object whose interior has some matter distribution should support fluid modes in addition to the conventional and universally present spacetime modes. The fluid modes oscillate at a lower frequency, decay at a slower rate and produce weaker gravitational waves than do those of the standard BH spacetime modes. Hence, they imprint a distinct signature of the interior in the gravitational-waves emitted from a BH merger. We find that interesting bounds can already be placed by current gravitational-wave observations and that future observations with Advanced LIGO's design sensitivity may allow the detection of the imprint of the interior modes.