Today I learned that TAS came out right after TOS... I always thought that TAS was a some retro thing that came out after ENT...
Pretty embarrassed
I guess it's easy to get confused these days, given how all the series are available at the same time, rather than one after the other.
It would have been impossible for TAS to be post-ENT, as Deforest Kelley died two years before Enterprise premiered. It's thanks to Leonard Nimoy that some of the other actors were allowed to voice their own characters. He pretty much said that if they weren't included, he wouldn't take part either. Sadly, they still wouldn't include Chekov, but Walter Koenig was allowed to pitch a script (which was made, but if memory serves it was a pretty ridiculous episode).
Some fans consider TAS to be the unofficial "rest of the 5-year-mission" begun in TOS, but officially TAS's canon status has varied according to the whims of Roddenberry and whichever network or studio has a current opinion on it.
I'd say its current status can most likely be considered canon to some extent, given the inclusion of pure-Vulcan bigotry toward Spock in nuTrek (there are scenes in the TAS episode "Yesteryear" when some of young Spock's classmates taunt him in some pretty blatant displays of racism).
On the other hand, if TAS were really considered canon, then Enterprise would have been about Captain Robert April (reference: "The Counter-Clock Incident") and the holodeck wouldn't have been this Amazing New Thing in TNG.
Fun TAS facts:
Uhura finally gets to be in charge.
One of the episodes is a crossover with Larry Niven's Known Space series.
There are sequels to the TOS episodes "The Trouble With Tribbles", "Shore Leave", "City on the Edge of Forever", and the Mudd episodes. "Yesteryear" can also be considered a prequel to "Journey to Babel."
The first holodeck was on Kirk's Enterprise, not Picard's.
TAS had the first Native American crewmember.
As with James Blish's Star Trek episode anthologies, the TAS episodes were adapted to short story form in a series of "Star Trek Log" anthologies, written by Alan Dean Foster. There were 10 books, and the final four were novel-length (Foster added a lot of original material to the single episodes in those books; the first six contained 3 episodes each).