The 21st Century AD, is what most people would label this year. It's a bit like our being in our tenth year when we're still saying we're nine year's old.
For example, we are not one year old when we are born, but we are IN our first year, i.e. we are living within the first twelve months of our life so we cannot claim to be one year old until a full year has passed from when we were born.
We passed the 20th Century behind us in 2000 AD - or may 1999 (there could be some debate here) That was the Twentieth Century - Hence 20th Century Fox films, for example. So, to reiterate, we're now in the 21st Century.