Pulsar Timing Array experiments exploit the clock-like behaviour of an array of millisecond pulsars, with the goal of detecting low-frequency gravitational waves. Pulsar Timing Array experiments have been in operation over the last decade, led by groups in Europe, Australia, and North America. These experiments use the most sensitive radio telescopes in the world, extremely precise pulsar timing models and sophisticated detection algorithms to increase the sensitivity of Pulsar Timing Arrays. No detection of gravitational waves has been made to date with this technique, but Pulsar Timing Array upper limits already contributed to rule out some models of galaxy formation. Moreover, a new generation of radio telescopes, such as the Five hundred metre Aperture Spherical Telescope and, in particular, the Square Kilometre Array, will offer a significant improvement to the Pulsar Timing Array sensitivity. In this article, we review the basic concepts of Pulsar Timing Array experiments, and discuss the latest results from the established Pulsar Timing Array collaborations.