Gravitational-wave astronomy will soon become a new tool for observing the Universe. Detecting and interpreting gravitational waves will require deep theoretical insights into astronomical sources. The past three decades have seen remarkable progress in analytical and numerical computations of the source dynamics, development of search algorithms and analysis of data from detectors with unprecedented sensitivity. This Chapter is devoted to examine the advances and future challenges in understanding the dynamics of binary and isolated compact-object systems, expected cosmological sources, their amplitudes and rates, and highlights of results from gravitational-wave observations. All of this is a testament to the readiness of the community to open a new window for observing the cosmos, a century after gravitational waves were first predicted by Albert Einstein.
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