Nationality, belonging, and cultural identity
At the very beginning of the movie, Wong includes shots of Fai's British National Overseas Passport as a way to indicate to the audience that this film will be dealing with issues of nationality.
Released in May 1997, intentionally before the handover of Hong Kong from the British to China on 30 June 1997 after 100 years of colonial rule, the film represents the uncertainty of the future felt by Hongkongers at the time. The film's subtitle: "A Story About Reunion" also implies that the film would comment on the handover. The inclusion of the date in the opening and the news broadcast of Deng Xiaoping's death on 20 February 1997 serve to place the audience explicitly in the time period immediately before the Handover of Hong Kong. Some have suggested that the English title of the film is in relation to the uncertainty around if Hong Kong and China would be "happy together" after their reunion.
In one interpretation, Po-Wing and Fai represent two sides of Hong Kong that cannot be reconciled: Po-Wing stays in Buenos Aires without a passport, like Hong Kong Chinese people who don't have a real British passport, representing an "eternal exile and diaspora". Fai, however, is able to see the waterfall and go to Taiwan but it is not shown whether Fai is able to reconcile with his father or not. Since Po-Wing wants his passport, meaning he wants to leave Buenos Aires, both main characters show that they feel uncertain about their place in the diaspora.
A different interpretation stated that Fai, a gay man, represents the social freedoms that Hongkongers possess and the runaway son who travelled to the other side of the world: Buenos Aires in the film and Britain historically. But, this son (Hong Kong and Fai) "must return and reconcile his differences with old-fashioned China," which is represented by Fai's father. Chang represents Taiwan, a country with a similar past as Hong Kong with China, who comforts Fai (Hong Kong), showing him that there is hope for the future. This hope is demonstrated through the increasing saturation of the film as Fai's life becomes more and more stable.
Wong's choice of Buenos Aires is particular because it is the antipode of Hong Kong, meaning it is on the opposite side of the world and in an opposite time. This had been interpreted as a place where Fai and Po-Wing were looking for the opposite of home and Hong Kong. They do not describe this as a political allegory but rather a questioning of cultural identity and the definitions of "home, belonging, and migrancy". Another interpretation viewed the scenes of Hong Kong shot upside down not as a political allegory either, but a way to show how far the characters were from their roots.
Similarly, the theme of displacement from Hong Kong to Buenos Aires interestingly emphasizes their similarities rather than their differences when compared to the shots of Hong Kong in Wong Kar-wai's previous films. Despite being on the other side of the world and far from their "home", the couple experiences the same problems, implying the inevitability of their relationship's deterioration. By emphasizing the similarities between these two places, Wong emphasizes the homelessness and lack of belonging of both Fai and Po-Wing.
Another theme of the film is the sense of confinement and claustrophobia that accompanies the sense of non-belonging of Fai and Po-Wing. This is conveyed through the shaky handheld camera, the small size, poor lighting, and dirtiness of Fai's apartment, the kitchen, alleys, the tango bar, the restaurant kitchen, and the public bathroom corridor. This confinement is also manifested through Po-Wing's confinement to Fai's apartment because his injured hands prevent him from taking care of himself. Later, Po-Wing is also confined to Buenos Aires because Fai refuses to return his passport. Yet, the imagery of the Iguazu Falls contrasts the theme of confinement with the symbolic openness of possibility and hope for Po-Wing and Fai's relationship.
One interpretation explained that the lack of a sense of belonging due to a combination of their marginal race, sexuality, and language in Buenos Aires and Hong Kong prevented Po-Wing and Fai from forming a stable relationship. This instability is in part shown through the instability of the camera in some shots, relating to the characters's inability to find their own place in the world. Neither place is welcoming and the couple experiences the same problems in both places.
The marginalization of Fai specifically is demonstrated by the way he visually cannot blend into the crowds and environments in Buenos Aires in comparison to Taipei. It is only in Taipei that Fai smiles, and it is implied that he feels a sense of belonging as he visits the Chang family noodle shop and takes the train. The movie does not definitively show that Fai returns to Hong Kong, making it possible that he stayed in Taipei, where he feels like he belongs and begins to have hope for the future.