Subjective precognition

"She can see into the future, although what she sees is based on decisions being made; thus, she must wait for a decision to be firmly rooted in the mind, or acted upon, before she can see the end result. Her talent is limited to humans and vampires because she has been both; she cannot see the futures of werewolves or hybrid vampires."

- Entry on Alice's gift

Precognition is Alice Cullen's ability to gain information using mechanisms other than the five senses.

Description
Alice can get visions of the future, sometimes at will. At first she couldn't control them, but she gained it during her growth as a vampire. She can use it to keep tab of things by merely focusing on the subject. She has also described that some visions come to her when there is a connection between her and the source of the vision; whether it be a threat to her family or simply someone she relates to.

Pre-Twilight
Though her creator was destroyed, Alice determinedly searched for the one person in most of her visions -- Jasper. After the two finally met, they searched for the Cullens, because they wanted to have a family and to help Jasper become 'more vegetarian'. They haven't left the family since.

Twilight
In Twilight, Alice sees Bella becoming a vampire, and that it would storm at the baseball clearing. She also sees Laurent, Victoria and James coming towards the clearing after they hear the game, but since it was a snap decision, there was no way to run or to hide Bella. After they run to Phoenix, Alice sees James meeting Bella at the ballet studio and at Bella's house. It can also be assumed that she also sees Bella running from Jasper, but that it was too late to stop her. When they get to the ballet studio, they save her even though she is severely injured. When recreating a scene for Bella's accident, Edward says "Alice had a little too much fun gathering evidence".

Midnight Sun
In Midnight Sun, Alice's visions are more clear as Edward sees them along with her. It is revealed that she saw him leaving, Tyler's car crash, Bella becoming her best friend, Edward supposedly killing Bella, Jasper's attempts to kill Bella, Edward blocking him, and, finally, Edward falling in love with Bella.

New Moon
In New Moon, Alice saw Bella jumping off a cliff, and assumed she had committed suicide because she couldn't see Jacob, him being a shape-shifter (though she didn't know it at the time). Alice becomes very uncomfortable when she can't see something because of a shape-shifter. She told Rosalie while she went to Forks to see Charlie, There, Bella who explained what she was doing and about the Quileute tribe. Later, Edward, posing as Carlisle, calls Charlie to check on Rosalie telling the truth about Bella being dead. Jacob answered and told Edward that Charlie was at a funeral. Alice revealed that Edward thought the funeral was Bella's, and that she really was dead. They rushed to Volterra, Italy, to prevent Edward from committing suicide as well, and Alice saw visions of him trying to think up ways to get himself killed, but his changing his mind so quickly made almost impossible for her to tell final decision. Bella managed to stop him in time, but they were all, including Alice, brought to the Volturi, who asked them to join. They declined. When Caius demanded Bella dead because of her knowledge of vampires, Alice shows Aro a vision of Bella becoming a vampire. They were then set free, and Alice later voted that Bella become a vampire.

Eclipse
In Eclipse, Alice sees a vision of Victoria being back in town. After Edward leaves Bella in her care, she sees her running off to La Push with Jacob, but cannot stop her. Afterwards, during the mysterious string of Seattle murders, the family realizes a vampire is behind it that knows of Alice's gift as they are changing their minds so fast. When they realize it's an army of newborn vampires, they start training and try to enlist the help of the Denali Coven. However they refuse since Irina is still upset over Laurent's death at the hands of the wolves. So, the wolf pack wind up helping, even though Alice cannot see them. Eventually, they realize Victoria is behind the army along with her new partner Riley and the Cullens wait up in the snowy woods to wait out the fight. Thanks to Alice's gift, the fight is successful and the Cullens win after Edward destroys Victoria, and Seth Clearwater destroys Riley. Before the arrival of the Volturi, it is revealed that Alice is irritated with Jasper as he wouldn't let her fight and, as a result, she bites him.

Breaking Dawn
During Breaking Dawn, Alice cannot see Bella because of her pregnancy with Renesmee, and most of the coven initially believes it's a boy. She explains to Jacob that it gives her a headache to try and see, and since she cannot see at all with him around, her headache gets lessened. After Renesmee is born, and Irina reports her to the Volturi, Alice and Jasper leave, instructing the family to gather as many witnesses as they can. Alice sends various others along on her travels, and eventually reappears at the final confrontation with several other vampires, and the hybrid, Nahuel. Nahuel informs the gathering that he, his sisters and Renesmee are not of any danger of exposure, and the Volturi leave in peace. When everyone confronts Alice about her disappearance, she apologizes and admits she took so long, because she was trying to look for what she couldn't see in her visions, like it was a blind spot.

Limitations
Her visions are subjective; she can only see the future once a decision affecting it has been made, and some visions are more certain than others. But the visions can change if the subject changes her/his minds, meaning sometimes it can change all too quickly for her to see clearly. If a decision still hasn't been made, her visions will remain fuzzy and unclear, and she will see different "pictures" until it's decided.

Her subjects can "hide" from her vision by being indecisive. The vampire Victoria evaded being seen while creating an army by letting someone else select her soldiers and remaining in the shadows.

She can see vampires and, less clearly, humans. However, she cannot see any visions involving shape-shifters or hybrids, because, as she says, "she had never been one". The closer, or 'attuned', she is to a person, the clearer she can see him or her.

In Eclipse, Alice explains that since her visions are no illusion of the mind, but rooted into reality, they can affect Bella. This is at a variance with the gifts, such as Jane's capability to inflict the illusion of pain, of other vampires that are connected to the mind.

It is also very likely that she cannot see any vision that involves real werewolves.

Origins
Alice was born with this power. Her predictions mostly manifested as feelings and only visions when the future was set. She had had this power since she was a child and was accused of being a witch or changeling because some people believed she had put a curse on them instead of believing that she was really seeing what was going to happen. At age 18, she had a vision of her mother's death and tried to keep her safe, until she eventually failed. As her father remarried within 6 months after her mother's death, she confronted her father about her suspicions, and then saw herself being killed and realized that she had turned to the wrong person.

Her father later accused her of having gone mad as a result of her mother's death and her visions, and demanded the county take her away. Alice was eventually admitted to an asylum where she received shock treatments that removed all of her memories.

Alice was saved by an unknown compassionate vampire, who changed her to protect her from the tracker James. Alice smelled beyond mouth-watering to James, so she was changed in order to prevent James from killing her.

Note
The fact that she was able to see James coming for her as a human is questionable. If her gift involves seeing humans and vampires because of her transition, she should not have been able to see vampires as a human. However, perhaps because humans can become vampires or werewolves through a bite, this allowed her to see James in some ways. This also suggests that her power involves seeing real werewolves as well, since a vampire's gift is only enhanced and not restrained by the transformation.