Spoilers ahead. Dark Phoenix, out June 7, tells the story of how Sophie Turner's Jean Grey absorbs a strange force on a mission to space with the rest of the X-Men that boosts her power and makes her dangerous to others. The film follows the comics arc The Dark Phoenix Saga, which ran over 10 issues in 1976 and 1980. But it makes a big change in introducing Jessica Chastain's character, a D'Bari alien named Vuk, in the guise of a human. In Marvel comics, the D'Bari aliens don't appear until after The Dark Phoenix Saga is complete. As per usual with comic book films, the new X-Men flick combines a few different D'Bari stories to serve Jean's narrative.
The D'Bari leader Vuk — a man in the comics — first appears in Avengers Vol 1 #4, from 1964, as an unnamed alien. Vuk's first X-Men appearance happened in 2000's Uncanny X-Men Vol 1 #387. That doesn't mean that Dark Phoenix changes everything about the comics' D'Bari storyline, however. The Dark Phoenix Saga includes Jean Grey destroying the D'Bari planet and killing most of the alien race. She doesn't do this in the film, but their planet's destruction is the reason the D'Bari come to earth to find her.
In the comics, when Jean Grey believes she killed Cyclops, she's overtaken by the power of the Phoenix and flies into the sky, landing in the D'Bari galaxy. Once there, as Marvel Wiki explains, Jean consumes the D'Bari system's star in order to re-energize herself, which causes a supernova explosion which, as mentioned before, kills almost all of the D'Bari people. As the Wiki states, the D'Bari who survive the explosion — because they weren't on their planet — "developed a hatred of humanity." It's not until the 2000 issue, Uncanny X-Men Vol 1 #387, that Vuk retaliates against Jean Grey for wiping out his people.
When Vuk meets Jean Grey in the comics he makes it clear that he only wants to get vengeance, and the D'Bari stage an attack against the X-Men on earth. While the D'Bari can use disguises in Marvel comics, they're not quite the shape shifters they seem to be in the movie. Per Marvel's Wiki, the D'Bari's powers allow them to live for hundreds of years and they have super-strength. As Digital Spy points out, the comics portray Vuk, under his alias Starhammer, wearing armor that makes him impervious to physical attacks. The Dark Phoenix film doesn't include this armor, nor does it show the the D'Bari as they appear in the comics, with light green skin and shaggy, green hair. They are briefly shown in their darker green, humanoid form. But for most of the film, they're in their human guise.
As important as Vuk is to the X-Men, the character also appears in two Captain America comics and three Sensational She-Hulk Marvel comics. The Skrulls, who you probably remember from Captain Marvel, also appear in those She-Hulk stories. Since the Skrulls are most likely going to appear in the MCU again, it's possible that the D'Bari may provide some sort of tie-in for the X-Men to meet the Avengers.
Then again, Marvel Studios president Kevin Feige told i09 that the X-Men joining the MCU won't happen for "a very long time." But the future is full of possibilities, including these fearsome aliens.