When did the third millennium begin?

This millennium officially began on: 1 January 2001 GMT

A brief history of the current calendar system

The simple explanation is that our Western calendar system began at 1 AD. There was no year 0. The calendar we use today goes from 1 BC straight to 1 AD.

The calendar base that we use today was not devised until the year 525 AD. At that time the Roman Calendar was still in use. It was based on the founding of the city of Rome on April 22, 753 BC.

The new calendar was conceived by a monk called Dionysius Exiguus. He proposed that Christ was born in the year of Rome 753 (but most historians agree that it should have been some years earlier).

The Venerable Bede, an English monk, through his writings in the 8th century, re-chronicled history. Up to that time people had been living, say, in the (Roman) year 1500. They suddenly found they were living in 747 AD.

You can read a more comprehensive explanation in the article about calendar systems.