Fans of Captain Marvel (aka Carol Danvers) or Rogue might be aware of the rivalry and messed-up history that exists between these two heroines. However, those who haven't read their respective comics may not be aware of the major events contributing to this long-running superhero rivalry -- which traces back decades.
The first time these two characters directly interact, in 1977's Ms. Marvel #18, by Chris Claremont and Jim Mooney, it sets the tone of their relationship for years to come. Rogue sweeps in, beats Carol unconscious and steals her powers. Then she dumps Carol's unconscious body.
Unfortunately, at the time, Rogue's control over her absorption powers is tenuous at best. She mistakenly holds onto Carol for too long, which results in Carol losing her memories as well as access to her powers, at least in the short term.
Initially, Rogue's attack seems completely unprovoked and confusing. After all, before this point, Carol has been missing in the Marvel Universe for quite some time. She isn't actively being a superhero, so targeting her seems cruel and unusual. Later, it's revealed that the crux of Rogue's issue with Carol involves another X-Men character: Mystique.
Mystique, the adoptive mother of Rogue, is one of those characters who never knows when to leave well enough alone. When Mystique learns that Ms. Marvel will someday cause harm to Rogue, she doesn't hesitate to act -- or rather, have Rogue act. She sends Rogue after Carol Danvers like a heat-seeking missile.
Carol does eventually regain her memories, though she no longer has emotional ties to them. While she can't feel anything for the memories that flood her mind, she feels the loss of those emotions keenly.
Given that information, it's no surprise that she takes the next bit of news poorly. The X-Men allow Rogue to join their team, even knowing full well what Rogue has done to Carol, who's part of the team herself. She leaves when Rogue joins.
Unfortunately, Rogue is struggling in her own way. Carol's memories remain locked in her mind, resulting in endless amounts of confusion; at times, she says she feels like she has two minds in one body. This can be attributed to the fact that Carol's personality sometimes becomes dominant. In fact, she can even don her old Ms. Marvel outfit -- which is confusing and weird for both Rogue and Carol.
Eventually, Rogue is able to shed this extra personality, but in doing so she also loses all of the powers she absorbed from Carol. Considering this grants her a new lease on life, it's a trade she's content to make.
Later, the two form a sort of truce, though it's tentative and fragile. They fight as allies on more than one occasion, though they also face-off against each other, most notably in Avengers vs. X-Men. Most recently, the pair fought in the first arc of the current Captain Marvel ongoing, though not of their own volition.
When Nuclear Man traps Carol and several other women on island in another dimension, he uses Rogue to fight Captain Marvel in order to learn who is stronger. It's a brutal battle, with Rogue once again absorbing Carol. However, this becomes an advantage for both women. They literally put their heads together and defeat the misogynistic foe. Moreover, the absorption isn't permanent -- both heroes are stronger and more in control of their abilities now.
The whole situation results in a much better understanding between the two. So while Captain Marvel and Rogue will likely never be friends, there is a stronger sense of camaraderie between them now than ever before.