Neutrinos are weakly-interacting neutral particles, which makes them powerful sources of information about the most energetic processes in the universe, such as the origin of ultra-energetic cosmic rays or gamma-ray bursts. However, a price must be paid in order to detect them: gargantuan detectors at the bottom of the sea or under the Antarctic ice are required. The detection of the first high-energy cosmic neutrinos in 2013 by the IceCube observatory represented the start of so-called neutrino astronomy, a new way of observing the universe, which can play a key role in future discoveries. In this article, we describe how neutrino telescopes work, as well as the different initial configurations that made this new twenty-first century astro...