John Byrne reinvented Superman in the '80s with a miniseries entitled The Man of Steel, something that should have been a giveaway that the studio was planning on using it in their new movie Man of Steel.
He has, generally, received very little credit for his contributions to the film. Some of the design elements call back to what Mark Waid and Leinil F. Yu did in Birthright, which is certainly part of it, as is probably the fact that Byrne isn't actively involved with either social media or the comics community in the way that Waid is. Still, though--there's a lot of Byrne in this movie.
Like, a lot.
Krypton is a cold, sterile world where natural births don't happen
If I remember my history correctly, Byrne's was slightly different from this in that you were permitted to give birth naturally, but nobody (including Jor-El and Lara) actually did it.
And, yeah, in The Man of Steel, Byrne had Kal-El in one of those little pods like the fetuses are developed in in Man of Steel. In fact, that's how Superman came to earth, with his "egg," called a genesis chamber, attached to the base of the rocket and blasted off to Earth. As a result of that, actually, there was even more emotional weight to the decision Jor-El and Lara had to make: "We'll never even get to touch him," or something along those lines.
Also: That headgear.
...Alright, so maybe not quite enough. There's more to it than just the headgear worn by the council in the movie. There's also the fact that a lot of Kryptonian culture that isn't key to Superman specifically (like the dragonfly-horse thing) originated in Byrne's The Man of Steel, the subsequent Superman series and its companion series The World of Krypton.
Clark Kent as The Blur
Okay, so they didn't ever call him by some clever name like they did in Smallville, but the idea of a non-costumed Clark Kent anonymously doing good deeds for strangers as he wandered the globe is something that was established during the Byrne era, too. In fact, in The Man of Steel #1 you can see an entry in Martha Kent's scrapbook (yes, just like the scrapbook in the movie) that hints we're very close to the same world indeed: the story of a collapsing bridge that suddenly holds just long enough for the workers to be evacuated certainly feels similar to what we saw on the oil rig.
As we've hinted above, this is a concept that got picked up and run with in places like Birthright and Smallville, and which has become a part of the mythology in the New 52 as well, but the first time I remember it was in the Byrne run.
The Crazy Kryptonian Dream Sequence
I think the most off-putting sequence in the film for me was the elaborate, Zod-induced fantasy in which Superman sinks into the mountain of skulls after he and the other Kryptonians are the instruments of Kypton's resurrection and humanity's destruction. In no small part, this weirded me out because it was filmed as a kind of oddball dream sequence rather than just expository dialogue or a computer display.
But that's not all that unusual. In The Man of Steel, that's how Jor-El first comes to Superman, creating an illusion of the Fortress of Solitude, of the last days of Krypton and more to expose Clark (then already Superman, since in The Man of Steel the costume is made by the Kents and the "S" is an S) to the world's history and doom. Superman, at first unable to understand Kryptonian, makes physical contact with his fully-interactive holo-dad and suddenly finds himself feeling dizzy and addled, able to undertand and speak the language but suddenly dressed as Superman and standing in the middle of a realistic fantasy.
Superman Kills Zod
Alright, so this one didn't happen during The Man of Steel--but it showed up in the movie and it's easily the most-discussed single moment in the film. So it seems worth mentioning that almost the exact same thing--the idea that Superman had to kill Zod because he was unwilling or unable to relent and would always be a threat, no matter what Superman did--was used in the Byrne run as well.
Of course, as we've discussed before, after Superman had to kill the Phantom Zone criminals, he was so torn up about it that he exiled himself in space, setting off a domino effect of story consequences for years to come. Which could be promising for a sequel.