Sometimes referred to as the "Noughties" (following on from the 80s, 90s, etc).

If it's a current piece you could refer to "the current decade" or "since 2000" or "this century" .

Not sure if ppl are also using "millenium" or "millenial" in this sort of context.

Good question, I think it's one a lot of ppl are having trouble with. There are a few art/history/journo types kicking around on BB so hopefully some of them will have some good answers!