Dan (Jude Law) is a young writer walking down a street in downtown London. He spots a young woman (Natalie Portman) walking in the opposite direction and they make eye contact and begin to smile at one another. Not being used to cars driving on the left side of the road in the UK, she steps into traffic and gets hit by a car. Dan runs to her side and she wakes up and says "Hello, stranger." She isn't badly hurt, and Dan takes her to the hospital where they start to get to know each other. As they're leaving the hospital, they pass by a park that Dan remembers from when he was little. They pass a wall and notice that it has the names of firemen, policemen, or anyone else who has given their life to save another person.
They get on the bus and continue their conversation. We learn that Dan is a wanna-be writer who daylights as an obituary writer. The young American woman introduces herself as 'Alice Ayres'. She claims that she is a stripper from New York City who has come to London to leave a bad relationship. They finally arrive at Dan's office. He says goodbye and starts to leave and then turns around. When asked if he has a girlfriend, he says "yes".
One Year Later.
Dan is having his photo taken in a small artists studio by Anna (Julia Roberts). Dan and Alice are living together, and Dan has written a novel about his romantic life with Alice. Anna is taken his photo for the dust jacket of his recently published book. Anna is an American photographer who mainly takes portraits of strangers. She mentions that she likes to go to the aquarium and possibly take photos of people there. She reveals to Dan that she's currently separated from her husband. He learns that shes read his book and likes it. They kiss one another and she learns that he's got a girlfriend and the book is based on her. She ends the kiss at the point, while he's professing that he likes her a lot and needs to see her. She tells him to get over it.
At this point the doorbell buzzes and its Alice, who has come to meet Dan having just gotten off her job at a local coffee shop. He lets her up to the studio where she and Anna meet. Alice asks Anna to take her photograph and Dan leaves so the two of them can be alone. She begins to take her photo and Alice reveals that she heard their conversation on the intercom when she was downstairs. She turns away and Anna begins to apologize. Alice turns back with tears in her eyes and yells at Anna to take the picture.
A little later, Dan is in his apartment on his computer. He's in a sex chat room and has logged on as a woman for a joke. He meets another man on the web who's name is Larry (Clive Owen). He's a dermatologist and a sex addic logging on while at work. When he asks Dan for a name, he tells him 'Anna'. They write some hot and heavy stuff back to one another and Dan offers to meet Larry in person as a joke. He tells him to meet him at the aquarium. Larry goes there the next day and Anna is there as a coincidence. He approaches her and they discover that Dan has played a joke on him. He's embarrassed, she's amused, and they start to hit it off.
Four months later.
Dan and Alice are getting ready to go to Anna's art exhibition. We also learn that Dan's father has just passed away, and Dan is going to the funeral in the countryside after the art exhibition. Alice wants to go with him and support him, but he wants to be alone. They go to the exhibition and see the photo that Anna took of Alice with tears in her eyes. While Alice is looking at it, she meets Larry. They have a brief discussion and mild flirtation, and she learns that Larry and Anna are dating when she comes over and greets Larry. During the conversation, Dan is clearly still infatuated with Anna, and she tells him and Alice how she and Larry met, and that they call him 'cupid'. We also learn that Dan's book failed and he is once again an obituary writer. A little later, Dan puts Alice in a taxi cab outside the building, pretending that he's heading straight to the funeral, when actually he goes back to talk to Anna again.
Another Year Later.
Dan comes into his apartment at first telling Alice that he's been at a business dinner. Finally, he admits that he's been seeing Anna and that they've been having an affair since the evening at the art exhibition. At the same time, Anna is in her apartment with Larry. They are married now and Larry has just returned from a business trip. She doesn't tell him anything at first. Larry says he can't stand lying to her and admits that he slept with a prostitute on his trip. She simply tells him it's OK and then it comes out that she's been having an affair with Dan. Larry is furious and asks her why she bothered to marry him. She says she tried to end it with Dan when she and Larry decided to get married, but it started up again. Larry wants explicit details about her and Dan and she gives them to him. He's furious and tells her to leave. Back at Dan's apartment, Alice is heartbroken and in tears. Dan tries to comfort her and apologizes for hurting her. She leaves the apartment and he has no idea where she's gone.
Six Months Later.
Larry enters a strip club for a drink and he spots Alice, who's working there as a stripper wearing a skimpy top, G-string and a pink wig. He arranges a private dance with her in room. She gives him one willingly. Afterwards, she flirts and smiles and tells him her name is 'Jane Jones' as part of the act. Larry is torn up about his recent divorce proceedings from Anna and gets frustrated that Alice plays with him and won't take him seriously. He says he wants to sleep with her and she tells him "no". Then he asks for a more intimate look at her, she does what he asks.
A Few Months Later.
Anna is rushing to meet Dan at a music concert. She apologizes for being late. They sit to have a drink and we learn that she met Larry earlier in the day to have him sign the divorce papers. A few moments later, Dan guesses that Anna slept with Larry that day, and he was right. A flashback shows the meeting earlier, and Larry saying that he will sign the divorce papers if she'll sleep with him one last time, she agrees. Anna says she did it to end the whole thing and that all Larry got was her body. Dan is still upset.
Another Few Months Later.
Dan storms into Larry's office and angrily reveals that Anna has left him and is back with Larry. Dan tries to confront him and claim that this is all Larry's fault, when Larry reveals that Anna never did file the divorce papers. She is back with Larry because she's doomed to be in rocky relationships because she's a depression junky, but he loves her all the same and wants to be with her. Larry is at first angry with Dan and then begins to pity him because Dan is truly heartbroken and starts to cry. He tells Dan to go back to Alice, and Dan reveals that he doesn't know where she is. Larry tells him about the strip club and assures him that he didn't sleep with Alice when he saw her there. As Dan is leaving, Larry tells Dan that in truth, he did sleep with Alice. Dan goes to the strip club and sees Alice dancing on the stage. They both make eye contact with each other and seem to appear happy to see each other once again.
Alice and Dan are in a hotel room near Heathrow Airport. They seem really happy together. She's planning to return to New York and has decided to take him with her as a treat. Alice notes that this is the day when they first met on that London street corner which was four years ago, and Dan remarks how time flies by so fast. Dan asks Alice if she slept with Larry, and she tells him that she didn't. He demands to know the truth. Eventually he leaves the room to get cigarettes and asks Alice for the truth when he gets back. He turns around on his way out and returns to Alice with a flower. She tells him that she's not in love with him anymore. She tells him she stopped loving him just now because he kept pressing about Larry. Finally she admits the truth: she and Larry did sleep together that night after they ran into each other at the strip club. Dan tells her he has known all along and has forgiven her already. He tells her that it doesn't matter and he loves her, but she's fed up and tells him to leave. She starts yelling at him and he slaps her. Shocked by this outburst of violence, Dan leaves the hotel room.
Alice arrives back in New York by herself. At the same time, Dan has remained in London. He passes the park from the first day they met and notices one of the names on the wall is 'Alice Ayres'. Back in New York, when "Alice" is going through immigration, we see that her real name on her passport is Jane Jones (the name she had given Larry when he had pressed her for her real name in the strip club). Jane/Alice walks down a busy street in New York, and then she crosses a street against the "Don't Walk" signal, reminding us of the opening scene when she carelessly crossed a street in London, was struck by a taxi, and met Dan. Nonetheless, she is back in her home country, to face an uncertain future... alone.