The direct detection of gravitational waves by Advanced LIGO and Advanced Virgo has opened up a new field on the intersection of fundamental physics, astrophysics, and cosmology. After a brief reminder of general relativity, I will derive the properties of gravitational waves at the quadrupole level, showing how they are generated, how they take energy away from a system, and what the general shape of the wave will be depending on the nature of the source. Going beyond the quadrupole approximation, I will also give a rough overview of how state-of-the-art waveform models are arrived at. Next I will turn to data analysis techniques, both for the detection of signals from coalescing binary neutron stars and black holes, and methods to extract parameters such as masses, spins, and other variables that can be accessed. An overview will be given of the various observational results that have been obtained in terms of testing the genuinely strong-field dynamics of general relativity, measuring the elusive neutron star equation of state, and cosmology. I will end with the science that will be enabled by future large observatories in space (LISA) and on the ground (Einstein Telescope and Cosmic Explorer).