Earlier this year, the Chinese government finally lifted its restrictions on the Hong Kong director Peter Chan’s 1996 film, “Comrades, Almost a Love Story.” Insofar as censorship ever makes for sound cultural policy, the reasons for blocking “Comrades,” a star-driven romantic comedy about two Chinese migrants who venture to Hong Kong and the United States, seem especially joyless. Its offenses are slight, couched in minor differences of speech and habit. Even the most ideological viewer would be hard pressed to interpret this as an aggressively political film. But one of the strangest aspects of the long-overdue release of “Comrades” was the decision to have the elven young Chinese heartthrob Luhan record a new version of “Tian Mi Mi,” the Teresa Teng song that gives the film its Chinese title.

Originally released in 1979, “Tian Mi Mi” was one of Teng’s greatest hits, a loungy ballad about someone with a sweet and disarmingly familiar smile. “Where have I seen you before,” Teng wonders, before remembering: “Ah—in my dreams.” Despite this sense of bewitched yearning, she sounds calm, curious, almost teasing. Or maybe she merely accepts a fate in which reunion is impossible. Teng’s songs play throughout “Comrades,” beacons of sorts which remind the luckless pair of one another as well as of the China they’ve left behind. At one point, they try to trade on this nostalgia, peddling bootleg Teng cassettes and posters to other down-on-their-luck migrant workers. It spoils nothing to note that the lovers of “Comrades” do eventually reunite. At the end of it all, they stand outside a store window in Manhattan, both regarding the same TV news report: Teresa Teng, their idol, has just passed away. It might be the saddest moment in the film.

Millions of people experienced some version of this moment when Teng died twenty years ago, of an asthma attack, while on holiday in Chiang Mai, Thailand. At the time, she was probably the most famous Chinese singer in the world. After winning a series of talent competitions throughout Taiwan, she dropped out of high school to pursue a career as a singer, earning her first recording contract in 1968. She was fifteen, blessed with a sweet and versatile style that moved easily between traditional folk and newer, jazzier pop styles. During the next two decades, as Taiwan became a leading exporter of Mandarin-language entertainment, she would become a superstar in the Chinese-speaking world. She also eventually became an icon throughout the rest of Asia, where her ability to sing in different languages helped to herald the era of region-wide pop superstardom that has become today’s norm.

Teng’s influence was particularly powerful in China, which her parents had fled after the revolution. As an index of personal desires and romantic possibilities, the Communist regimes would occasionally ban Teng’s music as decadent and pornographic. Her syrupy ballads came to represent a foil to Party chairmen like Deng Xiaoping, whose family name she shared. There was a popular saying that, by day, everyone listened to “old Deng” because they had to. At night, everyone listened to “little Teng” because they wanted to.

Last month, I visited the Teresa Teng Museum in Kaohsiung, a city in southern Taiwan near a military base, where her family had once lived. Her brother opened the museum five years ago; stacks of discounted 2010 calendars in the gift shop attest to the high hopes he had for this space, which sits along a row of warehouses and repair shops on the banks of the Love River. It’s one of two Taiwanese memorials to the island’s most famous export—the other is an ornate mountainside tomb just outside of Taipei. There is also a small memorial hall, consisting largely of items donated by fans, in Teng’s ancestral village in China, a place she never visited.

It was a muggy afternoon and almost unbearably hot inside the building, which was less a museum than a series of storage warehouses that had been opened to the public. It looked like someone had given up while unpacking. In the first room, there were yellowing posters, unopened boxes of merchandise, an old Mercedes-Benz sedan from a brief spell in France. None of Teng’s music was playing; instead, there was the sound of swiveling fans. My wife made out the muffled cries of Avril Lavigne in the distance, playing on the stereo at a neighboring tire shop.

Teng’s brother has said that he opened the museum to give fans insight into their idol’s everyday life. The second room was much larger, filled with old sofas and beds, shelves lined with miniature bottles of airline booze, display cases filled with jade bracelets, handbags, replica pistols, and toiletries. Every so often, a worn cutout of Teng herself would remind me that one person had amassed all this stuff. There were posters of Teng posing with rifles and entertaining Taiwanese troops. There were eyelash curlers, chopsticks, commemorative plaques, and, according to an online review, nail clippers. The last room of the museum was the gift shop, where an impressive range of things—coffee, holograms, iPhone cases, T-shirts, watches, 2010 calendars—featured the singer’s face.

Teng belongs to an older generation. “I don’t like pop music,” various relatives kept telling me when I told them I wanted to visit the Teng Museum. “But there was something different about her.” A Taiwanese songwriter once remarked that she was “seven parts sweetness, three parts tears,” echoing a famous saying about the ratio of Mao’s bad and good ideas. It was the quality of her voice—economical, confident, tinged with a bit of plaintive longing. She wasn’t the brashest singer, nor did she possess dazzling range—critics and fans referred to her style as “elegant whispering.”

Teng had a tremendous gift for capturing that kernel of prospective sadness at the heart of all great romance. I’ve always been mesmerized by the way she seems to be holding back on “The Moon Represents My Heart,” one of her greatest ballads. Her voice seems to vibrate softly until it dissolves into the weepy strings and synths in the background. It’s what made her special, a mastery of these tiny gestures that divine everyday sadness from private anguish. Her sense of melancholic restraint seems all the more wondrous when watching some of the amazing yet overblown covers of the song on YouTube.

Her music dripped with the possibility of freedom and choice, memory and longing. Perhaps they modelled a kind of voice that seemed unfathomable to some listeners, particularly those for whom simple, everyday desires could feel distant and dreamy. At times, her personal politics came to the fore. The daughter of a Taiwanese military official, she refused to play in China, even after restrictions on her music were lifted. During the Tiananmen uprising of 1989, she dedicated a series of concerts to the student protesters, lending new meaning to old songs like “The Moon Represents My Heart” or “My Home Is on the Other Side of the Mountain.”

There’s another popular saying: Wherever there are Chinese people, there is Teresa Teng’s music. I never appreciated her symbolism as a child, back when her music seemed soft and ubiquitous. But it’s not hard to imagine how Teng’s songs about love and distance spoke to the various migrations and political estrangements throughout the Chinese-speaking world. For immigrants throughout the Chinese diaspora, her music was a reminder of their journeys, an excuse to indulge in nostalgia, three or four minutes at a time.

Back at the museum, as if on cue, two busloads of tourists from Mainland China arrived. They didn’t seem bothered by the museum’s out-of-the-way location or its clutter and disarray. Instead, they moved through the halls in a tight pack. I joined them and listened to their guide, as he harangued them with wondrous tales of each item’s importance, after which they would photograph it. Here was Teng’s majestic music bringing the estranged people of China and Taiwan together—and, importantly, it was on the latter’s terms.