You can name a recent decade by calling it "the '60s", "the '80s", "the '90s", and so on.
Some people call the decade starting in the year 2000 "the aughts". "Aught" is a way of saying "zero". The decade starting in 2010 is "the teens".
You can also specify if something was at the beginning, middle, or end of the decade:
I used to live there in the late '70s.
I think that came out in the mid '90s.