Black Holes and Neutron Stars are some of the strangest objects in the universe, containing more mass than the Sun packed into a sphere only a few kilometres across. They are formed from the remains of high mass stars, which burn their fuel quickly and end their lives in supernova explosions which can outshine a whole galaxy. There are different types of supernova for different types of stars: their masses, spins and composition all play a role in determining their eventual fate, although the details are not fully understood yet. What is left over after the supernova is an object so dense that its gravity warps the space-time around it: a neutron star is thought to contain the densest possible matter, denser than an atomic nucleus, which is the only material strong enough to support the star against its own gravity. Even more extreme are black holes, which form when a star has even more mass, and neutron star matter cannot support its weight. When this happens the star collapses into a black hole, becoming so dense that not even light can escape the gravitational pull. At this point an event horizon forms, hiding its contents from the rest of the universe. Since black holes do not emit light, they are impossible for astronomers to find unless they are actively accreting material from a companion star. But there is another way to detect them using a completely new astronomical tool: gravitational waves. According to Einstein's theory of General Relativity, when black holes and neutron stars are found together in a binary system, the movement of so much matter in such a concentrated space creates vibrations in space-time itself. These travel out across the universe at the speed of light, changing the dimensions of everything they pass through, but invisible to the eye. Back on Earth, physicists have long been searching for gravitational waves by making extremely precise distance measurements using gravitational wave detectors. So far no signs have been found, but soon the Advanced LIGO and Advanced Virgo detectors will become operational with a sensitivity that ought to allow us to detect the gravitational waves from binary neutron stars within hundreds of millions of light years from Earth, and out to even greater distances for the heavier black hole binaries. The detectors are so sensitive that the change they can measure is equivalent of varying the distance between the Sun and Saturn by a hair's breadth. Encoded in the gravitational waves is information about the sources that emitted them, which will let us learn about the masses and spins of neutron stars and black holes. By measuring many signals, we will be able to piece together the physics that governs the evolution of massive stars, and how they end their lives.