Recent news about the upcoming Captain Marvel movie confirmed that a Skrull Invasion, led by Ben Mendelsohn's Talos, will threaten Earth in the film. First introduced in 1962's Fantastic Four #2, the Skrulls are actually a deviant strain of an earlier version of their race that was experimented on by the god-like Celestials. Their standard form is green-skinned and reptilian-like, but they have the ability to change their form to such a powerful degree that they can avoid detection by those with heightened senses and even telepaths. The ability of Skrulls to shape-shift has come in handy in their attempts to claim Earth as their own, though they've only really tried twice.
In their very first appearance, the Skrulls send a scouting team of four down from a mothership floating in orbit to clear the playing field for a full invasion. Their plan involves transforming into the Fantastic Four and tarnishing their reputations, ensuring that Marvel’s First Family is in no state to thwart their impending invasion.
The Skrulls succeed and even kidnap the Fantastic Four to make sure they don't get in the way. However, The Fantastic Four escape and overpower the unsuspecting Skrulls. Then the superhero team pretends to be the Skrulls (in their shapeshifted forms) and convince those on the mothership that Earth is too powerful to invade, showing them pictures of the monsters and giant ants that guard the planet (pictures taken from other Marvel comics, in fact!)
At the end of the issue, Reed convinces the remaining Skrulls on Earth to transform into cows before he hypnotizes them into forgetting their previous identities. The Skrulls are then left free to live out their days in peace on a farm. Following the Fantastic Four's bamboozling of the Skrulls on the mothership, the shape-shifters don't try another full Skrull invasion of Earth again for 46 years, with the release of 2008’s Secret Invasion.