Great King and the equivalent in many languages is a semantic title for historical titles of Monarchs, suggesting an elevated status among the host of Kings and Princes. This title is most usually associated with the shahanshah (Shah of shahs, i.e. king of kings, indeed translated in Greek Basileus toon basileoon, later adopted by the Byzantine emperors) of Persia under the Achaemenid dynasty whose vast empire in Asia lasted for 200 years up to the year 330 BC, and later adopted by successors of the Achaemenid empire whose monarchial names were also succeeded by "the Great". In comparison, High King was used by ancient rulers in Britain, Scotland and Ireland, as well as Greece.
In the 2nd Millennium BCE Near East, there was a tradition of reciprocally using such addresses between powers as a way of diplomatically recognizing each other as an equal. Only the kings of countries who were not subject to any other king and powerful enough to draw the respect from their adversaries were allowed to use the title of Great King. Those were the kings of Egypt, Yamhad, Hatti, Babylonia, Mitanni (until its demise in the 14th century), Assyria (only after the demise of Mitanni), and for a brief time Myceneans. Great Kings referred to each other as brothers and often established close relationships by means of marriages and frequent gift exchange. Letters exchanged between these rulers, several of which has been recovered especially in Amarna and Hittite archives, provide details of this diplomacy.
The case of Maharaja ("Great Raja", great King and Prince, in Sanskrit and Hindi) on the Indian subcontinent, originally reserved for the regional hegemon such as the Gupta, is a striking example how such a lofty style of this or an alternative model can get caught in a cycle of devalution by "title inflation" as ever more, mostly less powerful, rulers adopt the style. This is often followed by the emergence of one or more new, more exclusive and prestigious styles, as in this case Maharajadhiraja ("Great King of Kings"). The Turkic-Mongol title Khan also came to be 'augmented' to tiles like Chagan or Hakan, meaning 'Khan of khans', i.e. equivalent to king of kings.