  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.
