Long tails and streams of stars are the most noticeable traces of galaxy collisions. However, their tidal origin was recognized only less than 50 years ago and more than 10 years after their first observations. This review describes how the idea of galactic tides has emerged thanks to advances in numerical simulations, from the first simulations that included tens of particles to the most sophisticated ones with tens of millions of them and state-of-the-art hydrodynamical prescriptions. Theoretical aspects pertaining to the formation of tidal tails are then presented. The third part turns to observations and underlines the need for collecting deep multi-wavelength data to tackle the variety of physical processes exhibited by collisional debris. Tidal tails are not just stellar structures, but turn out to contain all the components usually found in galactic disks, in particular atomic/molecular gas and dust. They host star-forming complexes and are able to form star-clusters or even second-generation dwarf galaxies. The final part of the review discusses what tidal tails can tell us (or not) about the structure and the content of present-day galaxies, including their dark components, and explains how they may be used to probe the past evolution of galaxies and the history of their mass assembly. On-going deep wide-field surveys disclose many new low-surface brightness structures in the nearby Universe, offering great opportunities for attempting galactic archeology with tidal tails.