Pulsar Timing Arrays (PTA) use a Galactic-scale interferometer made of selected millisecond pulsars to detect low-frequency gravitational waves (GW) generated by coalescing supermassive black-hole binaries. The ensemble of low-frequency GWs introduce specific perturbations in the trains of pulsar signals that are angularly correlated among pulsar pairs in the sky. This correlation, that follows a tell-taling shape -- the Hellings and Downs curve -- is the main target of PTA searches. Its detection will open a new window in the GW spectrum, and a novel avenue to study supermassive black hole binaries. Recently, the European PTA (EPTA) and other worldwide PTA collaborations have detected a tantalising signal that appears to be common among all the pulsars in the networks, albeit uncorrelated. This has prompted additional, coordinated efforts to produce the most refined and sensitive PTA datasets to date, as well as new algorithms and statistical approaches, to tackle the real nature of this signal and achieve the first, low-frequency GW detection. In this talk, I will review the fundaments and state-of-the-art of the field, and detail the main results of the EPTA.