Dragon Ball Super's most important task is redeeming Vegeta - it might be the only significant character development that this series has going for it. Unlike Dragon Ball Z, which was all about the mutual progression and development of both Goku and Gohan, Dragon Ball Super has been much more about Vegeta's growth and evolution as a character - even though that progression often has to take a back seat to the spectacle of Goku's next big power jump. However, fans of Dragon Ball Super's anime have seen some major turns in Vegeta's character - and fans of the manga series have seen an even bigger transition into his own kind of hero.
At this point, every Dragon Ball fan knows how Dragon Ball Z took Vegeta from the role of a sadistic killer under Freeza's thumb, to being one of Earth's most important defenders. But at the same time, Dragon Ball Z always had Vegeta fight as something as a reluctant anti-hero, whose bravado was always shaping his motivations. It was only in the Majin Buu saga where we saw Vegeta really sacrifice his own life for a nobler purpose like protecting his family and friends.
Dragon Ball Super has seen Vegeta show off way more qualities of both a hero, a family man, and a friend. Not only that, but Dragon Ball Super has forced Vegeta to confront some of the darker points of his past - and his possible future and legacy, which has further shaped the Saiyan prince into a new kind of man.
It really started in the 'Resurrection F' story arc, in which Vegeta was given a new chance by Freeza to kill Goku and return to the evil emperor's service. Instead, Vegeta went Super Saiyan Blue and fought by Goku's side, ostensibly spitting in his old boss's face. Vegeta fought for his son Future Trunks in the hellish alternate future created by Zamasu/Goku Black, but his crowning moment was no doubt pushing past all limits in the Tournament of Power and unlocking Super Saiyan God Super Saiyan Evolution. Vegeta achieved that power on the strength of wanting to do whatever it took to defend his family, friends, and universe, and actually embracing that love and harnessing it (which is different than his self-sacrifice in the Buu saga). Even though Vegeta lost his fight in the ToP, his friends and teammates saw just how much heroic growth Vegeta has been through.
Dragon Ball Super's latest manga arcs have taken Vegeta's evolution much further. The Moro Arc brought Vegeta to New Namek to atone for his crimes against the Namekians (in Dragon Ball Z's Namek Arc), by fighting an ancient life-sucking sorcerer hunting the Namekian Dragon Balls. Vegeta didn't just fight - he made direct apologiesto the Namekians for his crimes. When New Namek fell to Moro, Vegeta traveled all the way to the Planet Yardrat to study and learn a new technique (Spirit Control) that allowed him to beat down Moro, and return all the lifeforce he stole back to New Namek. Vegeta literally balanced his Karma by resurrecting the people he once helped kill. Now, the latest Granolah Arc has seen Vegeta go so far as jumping in to save Goku during a one-on-one battle, pretty much cementing their brotherly bond (in case it was ever unclear).
The best things Dragon Ball Super has done with Vegeta's evolution is make sure that at his core, he's still Vegeta. While Vegeta is closer than ever with Goku, he's also committed to getting out of Goku's power-up shadow, and has developed his own unique techniques and power-ups. While Vegeta has more love than ever inside him for his family, friends, adopted planet and even the whole universe, he's still learning the power of a Destroyer God from Beerus. He's only grown bigger, and never lost what we loved about him in the first place. It's a character story that Dragon Ball Super needs to payoff in a big way.