Millennial typically covers people born from the early 80's through the 90's. The oldest millennials are about 36 right now.
The point remains, however, is that the span is too great for a single term to define them to any degree whatsoever.
I thought it was people born after the turn of the millenium.
What happended to "gen Y"?
Note that if you're in the older end of the cohort (mid-30s), there's some effort to rebrand those as 'Xennials', if for some reason you're really bothered by being called a millennial :)
This is why there is a Generation X/Millennial "transition" group of people that is sometimes referred to a Xennials[1].
'Millennial' seems to have been the catchier name, so it stuck around more - I think most people who are Millennial or Gen Y are also the other.