At the forefront of observation astrophysics is the direct detection of gravitational waves. The recent discoveries by the LIGO/Virgo collaboration has not only shown a key piece of Einstein's general theory of relativity to be correct, but they have heralded the era of gravitational-wave astrophysics, opening an entirely new and exciting window to our Universe — one that cannot be observed with traditional telescopes. In this lecture, I will introduce gravitational waves, what creates them, how they are detected, and what we can learn from their observation. I will also discuss other ways in which we are working to detect gravitational waves that will allow us to investigate astrophysical phenomena in new ways. This includes the observations of pulsars — highly dense stellar remnants — in a Galactic-scale gravitational-wave detector.