Nowadays the more powerful method to detect extrasolar planets is the transit method. We review the planet transits which were anticipated, searched, and the first ones which were observed all through history. Indeed transits of planets in front of their star were first investigated and studied in the solar system. The first observations of sunspots were sometimes mistaken for transits of unknown planets. The first scientific observation and study of a transit in the solar system was the observation of Mercury transit by Pierre Gassendi in 1631. Because observations of Venus transits could give a way to determine the distance Sun-Earth, transits of Venus were overwhelmingly observed. Some objects which actually do not exist were searched by their hypothetical transits on the Sun, as some examples a Venus satellite and an infra-mercurial planet. We evoke the possibly first use of the hypothesis of an exoplanet transit to explain some periodic variations of the luminosity of a star, namely the star Algol, during the eighteen century. Then we review the predictions of detection of exoplanets by their transits, those predictions being sometimes ancient, and made by astronomers as well as popular science writers. However, these very interesting predictions were never published in peer-reviewed journals specialized in astronomical discoveries and results. A possible transit of the planet beta Pic b was observed in 1981. Shall we see another transit expected for the same planet during 2018? Today, some studies of transits which are connected to hypothetical extraterrestrial civilisations are published in astronomical refereed journals. Some studies which would be classified not long ago as science fiction are now considered as scientific ones.

Submiited to Handbook of Exoplanets (Springer)