A modern Olympiad refers to a four-year period beginning on the opening of the Olympic Games for the summer sports. The first modern Olympiad began in 1896, the second in 1900, and so on (the 31st began in 2016: see the Olympic Charter).
An ancient Olympiad was a period of four years grouped together, counting inclusively as the ancients did. Each ancient Olympic year overlapped onto two of our modern reckoning of BC or AD years, from midsummer to midsummer. Example: Olympiad 140, year 1 = 220/219 BC; year 2 = 219/218 BC; year 3 = 218/217 BC; year 4 = 217/216 BC. Therefore, the games would have been held in July/August of 220 BC and held the next time in July/August of 216 BC, after four olympic years had been completed.
The sophist Hippias was the first writer to publish a list of victors of the Olympic Games, and by the time of Eratosthenes, it was generally agreed that the first Olympic games had happened during the summer of 776 BC. The combination of victor lists and calculations from 776 BC onwards enabled Greek historians to use the Olympiads as a way of reckoning time that did not depend on the time reckonings of one of the city-states. (See Attic calendar.) The first to do so consistently was Timaeus of Tauromenium in the third century BC. Nevertheless, since for events of the early history of the games the reckoning was used in retrospect, some of the dates given by later historian for events before the 5th century BC are very unreliable. In the 2nd century AD, Phlegon of Tralles summarised the events of each Olympiad in a book called Olympiads, and an extract from this has been preserved by the Byzantine writer Photius. Christian chroniclers continued to use this Greek system of dating as a way of synchronising biblical events with Greek and Roman history. In the 3rd century AD, Sextus Julius Africanus compiled a list of Olympic victors up to 217 BC, and this list has been preserved in the Chronicle of Eusebius.
An Olympiad started with the holding of the games, which occurred on the first or second full moon after the summer solstice, in what we call July or August. The games were therefore essentially a new years festival. In 776 BC this occurred on either July 23 or August 21. (After the introduction of the Metonic cycle about 432 BC, the start of the Olympic year was determined slightly differently).
Though the games were held without interruption, on more than one occasion they were held by others than the Eleians. The Eleians declared such games Anolympiads (non-Olympics), but it is assumed the winners were nevertheless recorded.