The initial premise is flat-out brilliant. In our reality, there really was a Project Orion in early planning stages in the late 1950s/early 1960s for a kind of space craft that could literally travel to other stars - which, well, never got off the ground. Ascension is in effect about an alternate reality in which it did, via a starship known as Ascension, and its multi-generational voyage to the Alpha Centauri star system. More specifically, the voyage is to a planet around Proximi Centauri (one was apparently discovered there last year, and, for that matter, such a planet is also the destination of my own 2002 science fiction novel, Borrowed Tides). Alpha Centauri, though the star closest to our Sun, is still more than 4 light years away, which is why the trip has to be multi-generational.
In the case of Ascension, the trip requires three generations, and we join the voyage midway, with the second generation in charge, and already having children. Since the ship left Earth in 1962, its culture is completely in that milieu, with talk of Marilyn and Elvis, and recordings of television shows and movies from that era as entertainment. As I said, this part of Ascension is outstanding. [Spoilers ahead]
Unfortunately, we learn all too soon that the Ascension starship has really gone nowhere - never left Earth - and is instead a daring experiment to see how generations of humans could survive in space. In effect, this makes Ascension a kind of Biosphere II - interesting, significant, but not as daring as if the ship were actually on its way to Proxima Centauri.
We've encountered twists like this before - most famously in Ender's Game - and they can be powerful. In Ascension, the twist is stunning - for a few minutes, until you get used to it, and then we have a very different kind of story. The murder on the ship becomes less of a mystery, because if the starship never left Earth, the murderer could have snuck on board any time. And the frantic story of people in high levels of national security on Earth, for or against the phony mission, is also something we've seen a lot of.
And the denouement, of a star child produced on the ship, developing extraordinary power which, if I understood the ending correctly, can hurl a person to Alpha Centauri without a space ship - well, this changes the whole narrative into something which is no longer plausible science fiction, and is also trite to say the least.
But the action is fast and compelling, and you do care for most of the characters, so I'd say - but all means see Ascension. Hey, I'd eve be up for a second season.
another voyage to Proxima Centauri - in the 2020s