How does the show connect to the DC movies and TV shows?
Though developed by David S. Goyer, screenwriter of Man of Steel and Batman v. Superman: Dawn of Justice, Krypton isn't technically set in the DC Extended Universe, although, according to Screenrant, earlier trailers included since-edited scenes that directly tied the series to the films. (The El family emblem, for instance, used to match the logo seen in the movies.)
Krypton is also separate from The CW's "Arrowverse" shows -- Arrow, Supergirl, The Flash, and Legends of Tomorrow -- which are also based on DC characters and have featured Superman in select episodes.
Showrunner Cameron Welsh told Digital Spy that the series is instead "adjacent" to both properties. "It's not part of the Arrowverse, and it's not really part of the DCEU," he admitted. "It's not going to feel like something completely different, or like it doesn't belong. It does [belong]. But by virtue of the fact that it's set on an alien planet and it's set 200 years ago, it's going to feel different in that sense."
Instead of fitting into those pre-existing worlds, the look of the show is more influenced by series like Game of Thrones, and the storytelling borrows beats from movies like J.J. Abrams' 2009 Star Trek and even Rogue One, in that it introduces time travel to set up new possibilities and focuses on characters whose fates are seemingly determined. Welsh himself admitted to the touchstones: "The world of Krypton will feel a lot more like Rogue One – it's a little bit less slick, a touch darker."