After revealing to Kara (Melissa Benoist) that Lois (Bitsie Tulloch) was pregnant in the final moments of the "Elseworlds" crossover last year, a promotional photo from "Crisis on Infinite Earths" suggests that this season's crossover will include the first appearance of the Super-Son, Jonathan Kent. The baby, born in the comics during the Convergence event, has gone on to become a major player in the DC Universe. After teaming up with Batman's son Damian Wayne, Jonathan was taken into space by his grandfather, Jor-El, who kept him there and raised him from age ten until his late teens. When he finally returned, he was old enough to leave again and go to the future to join the Legion of Super-Heroes.
In the Arrowverse, it seems likely that will play out somewhat differently. The CW is reportedly developing a spinoff series featuring Superman and Lois Lane, which will explore the unique challenges of being parents while one of them is one of the world's most celebrated reporters and the other is the world's best-known superhero.
Before Smallville, the last time Superman had a TV show (and arguably the last time there was a real Superman show, since Smallville had the "no tights, no flights" rule) was Lois & Clark: The New Adventures of Superman. That series as originally conceived as even more Lois-centric than it ended up being, with a heavier focus on the Daily Planet than the final series had. A series tentatively titled Metropolis was originally in development for DC Universe. That series, which was cancelled around the same time Swamp Thing became a reality, would have centered on Lois Lane and Lex Luthor and dealt with how everyday humans lived and worked in a world where Superman existed.
Given the prevalence of the multiverse in the Arrowverse and the potential consequences of having "Crisis on Infinite Earths" realign some things -- a lot of fans are still hoping that it could bring Supergirl to Earth-1 -- it is worth noting that following the failure of DC's New 52 publishing experiment, which rebooted the DC Universe as younger characters with less baggage, a series titled Superman: Lois and Clark came out from Dan Jurgens and Lee Weeks, dealing with a version of Superman and Lois who had been secretly living on the rebooted Earth, married and with a baby, for years, quietly righting wrongs without letting the world know they were around.
Recent rumors have suggested that Henry Cavill is finished as Superman, and that it may be years before the character gets another theatrical film. Meanwhile, Supergirl is a character supposedly being floated as a potential replacement for the Man of Steel in the DC film universe. Superman & Lois would technically be a spinoff of Supergirl, following on the heels of Green Arrow and the Canaries, a new series spinning out of Arrow and starring Katherine McNamara as the titular Arrow.
It is likely that fans will get more of a sense for what a Superman & Lois series might look like during "Crisis on Infinite Earths" later this winter.