In the sense of the Common Era calendar the third millennium began on January 1, 2000 and will end on December 31, 2999. The majority of the celebrations for the start of the third millennium occurred at midnight on December 311999 / January 12000. The first decade of the new millennium (see below) contains the year 2000.
Events
It's too early in this millennium to have enough perspective to see which of the events that have occurred so far will be considered sufficiently notable to rank as major events of the millennium, if any. However, some events are listed in the article on the 21st century.