I've been qualifying it, since we entered the 21st century. Otherwise it's not clear at all.
"Turn of the 20th century" is exactly what I say and write (if that's what I mean.
I don't use "Turn of the 21st century" as much. To be clear, I would use "the new millennium" preferably.
The harder question? What do you call this decade? Radio stations chicken out on it, when they say they play music from the '80s, '90s, and... "today." What the hell is "today?" They mean the "aughts" or the "zeros?" It will be an issue when we enter the "teens." Then you can't just call this current decade "today" anymore.
"Jaws is the Citizen Kane of movies."
blocked: logan2, Diamonds3, Hamilton22