Currently we use Anno Domini (A.D.) year numbering, sometimes secularized as "BCE" (Before Common Era) or "CE" (Common Era). What was the prevailing method of dating years in Western culture before this system came into use?
Prior to the adoption of the Anno Domini system, the main system of naming years was to refer to them as a given regnal year of the local ruler, or of a dominant nearby ruler (eg. the Roman Emperor). Specifically in Roman-dominated areas, the year was named after the two Consuls who took office that year. In a sense, Anno Domini is simply an extension of this, counting years of the "reign" of Jesus Christ.
If the Anno Domini system hadn't been adopted, the United States might refer to the current date as "December 13 of the sixth year of the Obama Presidency", while the British would describe it as "December 13 of the 62nd year of the reign of Elizabeth II".
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The use of Anno Domini ("in the year of our Lord") was first used in narrative history by Bede (although it had been used very slightly in some annals before that). It was invented, more or less, by Dionysus Exiguus (circa 470 – 544). Before Bede's use of it, there was no use of a year number in everyday use in western Europe. In other words, Anno Domini dating was original. The normal mode of specifying the year before that time (8th century) was by regnal years, or consular years (Rome), or Judges/Archons/Olympiads (Greece). Note that ancient historians sometimes used the Era of Nabonassar to do synchronisms.
When Rome collapsed and the consular dates no longer could be used, the Eastern (Byzantine) Empire adopted at first the era Anno Mundi beginning on 25 March 5493 BC, developed by scholars in Alexandria around 200 A.D., and now known as the "Alexandrian Era." Anno Mundi ("year of the world") posits a "date of creation" going forward from Adam and Eve. Later, in the 7th century, the Byzantines adopted a different Anno Mundi system based on the year 5509 B.C. and beginning on September 1.
Ab urbe condita, from the foundation of Rome, which is 753 BC.