| Summary: | Only a few years after the first detection of gravitational waves from coalescing stellar-mass black holes, the field of gravitational-wave astronomy is now firmly established after the detection of several more. These discoveries have opened up a new window onto the universe, which allows us to probe gravity and astrophysics in some of the most extreme environments in the universe. The detection and, in particular, the subsequent inference of the binaries' properties rely heavily on theoretical models of the signals. In this review, we first discuss the techniques used to model the gravitational-wave signals from coalescing black holes, before we summarize the observations made to date. We conclude with a brief outlook onto the prospects for binary black hole observations in the future.
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