The history of cometary astronomy is naturally divided into five major periods, the transitions being marked by important new insights. Before 1600, comets were essentially considered to be heavenly omens and were not yet clearly established as celestial (astronomical), rather than meteorological phenomena in the terrestrial atmosphere. Then followed two centuries of mostly positional measurements with emphasis on the motions and the orbits, lasting until the early 19th century, when the era of cometary physics was inaugurated, in particular by the passage of P/Halley in 1835. The next major step forward occurred in 1950 with the sudden emergence of the modern picture of comets as being essentially very old solar system objects made of primordial ice and dust, generally in unstable orbits and intensively interacting with the solar electromagnetic and corpuscular radiation. Finally, the space missions to P/Giacobini-Zinner in 1985 and especially to P/Halley in 1986 provided the first in situ observations of comets and dramatically widened our scientific horizon, but also posed many new questions which are yet to be answered.