This page contains information regarding new Star Trek material, and thus may contain spoilers.
Doctor Carol Marcus was a Starfleet science officer who served aboard the USS Enterprise from 2259. The daughter of Admiral Alexander Marcus and a woman with the maiden name Wallace, she had a doctorate in applied physics, specializing in advanced weaponry.
When Captain James T. Kirk set off for Qo'noS to find the traitor John Harrison, Marcus boarded his shuttle under the name Carol Wallace, using her mother's maiden name and claiming Admiral Marcus had assigned her. Spock deemed her credentials impressive but decided she was redundant, as he himself had been reinstated as first officer of the USS Enterprise. On the other hand, Kirk welcomed her aboard.
Spock confronted Marcus about her name not being in the ship's records, so Marcus apologized for the deception, explaining she had used her mother's maiden name to board the ship and examine the seventy-two experimental photon torpedoes her father had given Kirk to fire on Harrison. Spock informed Kirk about the deception, following Harrison's apprehension.
Marcus went with Leonard McCoy to examine a torpedo on a deserted meteor. McCoy accidentally activated the torpedo and trapped his hand, but despite Kirk's orders to beam her up, Marcus deactivated the torpedo before the emergency beam-up became necessary. Opening up the dormant torpedo, Marcus and McCoy discovered a cryogenically frozen man inside.
When questioned, Harrison revealed he was Khan Noonien Singh, revived to help prepare for war with the Klingon Empire, and that he had planned to smuggle his fellow Augments in the torpedoes before he was caught. Admiral Marcus appeared in the USS Vengeance, a warship designed by Khan, and began firing on the Enterprise. Carol Marcus revealed her presence to him in an effort to persuade her father to cease the attack, but he simply beamed her up and carried on. When taken to the bridge, Carol Marcus smacked her father but he ignored her, claiming the cover-up was necessary.
Scott deactivated the Vengeance's weaponry, giving Kirk and Khan time to fly to the ship and commandeer it. When they arrived on the bridge, Scott shot to stun Khan while Kirk admonished the admiral for compromising Starfleet. However, one shot was ineffective to keep Khan down, and he promptly beat Scott and Kirk. He then turned to Admiral Marcus, who tried to flee into the turbolift: Carol tried to stop him, but he responded by breaking her leg. Then he grabbed her father and crushed his skull before her very eyes, and she responded by screaming in horror.
Khan beamed Carol Marcus, along with Kirk and Scott, into the Enterprise's brig. Kirk brought her to sickbay for McCoy to patch her up. Khan resumed bombarding the Enterprise, and the damage caused the ship to fall to Earth. Kirk went into the warp core and reactivated the engines, preventing the Enterprise from crashing, but at the cost of poisoning himself. Marcus watched as Kirk's unconscious body was brought to sickbay. However, McCoy realized Khan's blood could be used to heal him. He and Marcus placed Kirk in one of the augments' cryotubes to put him in suspended animation. Spock and Uhura beamed down to apprehend Khan, after he crashed the Vengeance into San Francisco, and the blood transfusion proved successful.
A year later, Marcus attended an anniversary memorial for those killed by Khan and her father. She continued serving on the Enterprise bridge as science officer when it embarked on the first five-year mission. (Star Trek Into Darkness)
"I am ashamed to be your daughter."
- - Carol Marcus to Alexander Marcus on Marcus' actions (Star Trek Into Darkness)
"Dr. Marcus! I'm glad you can be part of the family."
"It's nice to have a family."
- - James Kirk and Carol Marcus on Marcus joining the Enterprise crew. (Star Trek Into Darkness)
A young Carol Marcus was in an early script draft of the film Star Trek. She would have been represented as meeting Kirk during his adolescence and living near him.  Co-writer Roberto Orci explained, "We wanted to potentially lay down the foundation for [their] friendship [....] And then literally because of the nature of the introductory story and making sure that our core group of characters had the proper amount of story that they deserve, she went into the potential future draft." 
Scotty actor Simon Pegg was thrilled to discover that Carol Marcus is involved in Star Trek Into Darkness. "Looking at it from the outside," Pegg recalled, "when I first saw her name in the script, it was exciting, 'cause Carol Marcus is a figure from Star Trek history."  Kirk actor Chris Pine once referred to the character, as written for Into Darkness, as "a really interesting part." (SciFiNow, issue 80, p. 23)
In Star Trek Into Darkness, Carol Marcus was played by Alice Eve. It was the people involved in the project that drew her to it, rather than any familiarity with Star Trek, which she didn't know much about before taking the role.  "I didn’t know who Carol Marcus was," she admitted. 
Alice Eve was likewise unaware, when she auditioned for the part, that it was the role of Carol Marcus she was trying out for. Although no full script was yet available, Director J.J. Abrams sent some scenes to her.  "I got a few pages of this character’s scenes and a scene that was kind of imagined, that wasn’t in the movie," remembered Eve. "It was just so well constructed and so well imagined and so truthful that I wanted to be part of this group of people that told stories in that way." The audition scene that is not in the movie was, in Eve's words, "an extended dialogue scene" between Carol Marcus and her father. The scene (whose plot points were included elsewhere in the film) was helpful to Eve in her understanding of Carol Marcus.  In fact, despite not knowing the name of the character she was auditioning to play, Eve got a distinct impression of the role from the collection of scenes, later stating, "I got a sense [that] [...] the journey of the character [J.J.] wanted was a girl who was struggling with her relationship with her father." Eve also consistently assumed that it was an already established character she would be playing, rather than a brand new one. 
The news that Alice Eve was cast in the part extremely excited Simon Pegg.  "I think I maybe got the job because I naturally speak very fast," reckoned Eve; she implied that the quickness of her speaking worked well in sync with J.J. Abrams' thinking, observing that he thinks "very fast." (Empire, Issue 287, p. 92)
As Alice Eve naturally has an English accent (though can do a considerably convincing American one) whereas the original portrayal of Carol Marcus featured an American accent, there was "ample discussion," said Eve, as to which accent Marcus was to have in Star Trek Into Darkness. Ultimately, Eve was allowed to portray the character with her own accent, later quipping, "The association sometimes is that English people are more intelligent than Americans. Of course, it isn't true, but I think we decided to play into that stereotype... because she is such a super-brain." 
Once Alice Eve found out which character she had been selected to depict, Eve was happy to have been cast as Carol Marcus. This was because the vast differences between how she had been written in Star Trek Into Darkness and her previous presentment meant that Eve didn't have to copy that earlier portrayal.  Nevertheless preparing for the role by watching every episode of Star Trek: The Original Series' first season and Star Trek II: The Wrath of Khan, Eve took certain cues from the prime-universe version of Marcus, saying, "Oh, it’s information you have to carry, definitely. It doesn’t shape it, but it will maybe inform certain choices." Eve kept in mind that Marcus was originally depicted as being "cleverer than Kirk." However, believing that the same version of the character has "great composure" – brought about by age as well as by lost aspirations and relationships – Eve found that she had to temper this characteristic to play a younger, less experienced Carol Marcus. Outlining the qualities that she kept in order to portray Marcus, Eve noted, "Her composure and her conviction and her thoughts, her belief in her intellect." 
Hair Department Head Mary L. Mastro was conscious of styling Alice Eve's hair, for her role as Carol Marcus, in such a way as to be similar to that of the character's initial representation. "Alice doesn't look anything like the person who originally played that role," observed Mastro, "but we wanted to give her a sensibility that was similar, yet not have it be that period." 
Alice Eve found that portraying the sexual chemistry between Marcus and Kirk came naturally to herself and Chris Pine, mainly due to him having blue eyes that she found "really beautiful."  The actress also appreciated that, while Marcus took "great" support from her relationship with Kirk, their bond didn't define Marcus and that she "was a very determined woman in her own right, dealing with her own struggles." 
Showing Carol Marcus changing into her flightsuit was motivated by J.J. Abrams wanting to appeal to Star Trek's male fanbase, which is fairly large.  When asked whether she found portraying this scene awkward, Alice Eve replied, "That's always an experience. I enjoyed working with everyone very much, I felt very comfortable in that environment and we'd all been training incredibly hard to, like, look like we were capable of living in space and saving the world. So, you know, I enjoyed the whole process of making that film, it was a good one." 
Carol Marcus is highlighted in a deleted scene from Star Trek Into Darkness, which explains the split universe's Carol was raised by her mother in England, thereby addressing why she has a different accent from her prime-universe counterpart.  This deleted scene is the only one involving Carol Marcus. 
Alice Eve has expressed happiness with her initial movie appearance as Carol Marcus, saying, "I really enjoyed the character I got to play."  She has also expressed happiness that the alternate reality take on the character has been intriguing for online fans. "It's good to know that people are interested in Carol Marcus," she said. "I was really glad to be able to play her, with her intelligence and her quick wit with Kirk." (The A-Z of Star Trek, SFX Special Edition 61, p. 63) Eve also requested that there be an action figure showing herself as Dr. Marcus, remarking, "I would like one." 
An image of Carol Marcus wearing only her underwear, from the scene in which she changes clothes, circulated around the Internet. There are mixed opinions about the scene, one criticism being that it undermined Marcus as a character. 
Alice Eve has stated that, should she return as Carol Marcus in another film after Star Trek Into Darkness, she would "like to see Carol take the (captain’s) chair for at least an hour." The actress has been noncommittal about the story points relating to Marcus' relationship to Kirk, observing that the alternate reality leaves it open as to whether they eventually have a child, as in the prime universe. "I’d love any eventuality with Carol," Eve commented. "I love playing her. I love her strength and independence of mind. So I’d like to continue to see that."