EXACTLY when does the 20th century end and the 21st century begin? The 20th century ends at midnight on December 31, 2000. January 1, 2001, will be the first day of the new century, and the new millennium. If that does not sound right, consider: the first year ended December 31, AD 1.; the second year ended December 31, AD 2; the 100th year (and the first century) ended December 31, AD 100. The last year of every century since has ended in '00, not '99. But do not expect anyone to wait until 2001 to celebrate the new millennium. Count on the world to herald the arrival of the 21st century on January 1, 2000.