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You may have seen a few South Korean romance shows pop up on Netflix recently and not given them a second thought. But a wave of appreciation for South Korean entertainment and culture is sweeping the world — a phenomenon known as hallyu — and American viewers are surfing the tide.

Entering the unpredictable world of K-drama, as the shows are called, you’ll need to throw your TV rule book out the window. In this seemingly lawless universe, plot lines ricochet from tragedy to comedy, sometimes spending just a little too long in the theater of the absurd. Expect hilarious chase scenes followed by unexpected dance routines, followed by Cinderella endings and thoughtful insights into South Korean life. It’s also ten-tissue fare, with lighthearted antics melting into heart-wrenching tragedy. The catharsis of a proper K-drama binge can rival that of any late-night karaoke-and-tambourine session.

K-drama is big business, with production houses vying for big-network attention and fans who are eager to buy anything K-drama related or endorsed. Little wonder that Netflix and Hulu added a flood of K-drama last year to their domestic libraries: Large fan bases have long existed in Asia, the Middle East and Latin America, and providers are betting that American audiences will follow suit.

Other streaming sites exist that stream mostly Asian content, and they offer far more titles, including movies. Of those, DramaFever provides the most engaging curation of recent shows, with Viki and Kocowa close behind. All three offer some content free with commercials, as well as free monthlong trials of premium subscriptions. At DramaFever, an ad-free plan is $4.99 a month or $49.99 a year; a basic Viki subscription is $4.17 a month or $49.99 annually; and an ad-free Kocowa experience costs $6.99 a month or $69.99 a year.

However you stream it, there’s a lot of great K-drama to sift through. Here’s some of the best.

If You Like Coming-Of-Age Stories

Lee Hye-ri in “Answer Me 1988.” CJ E&M

‘Answer Me 1988’

Where to stream: DramaFever, Viki

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Eighties nostalgia has taken root in South Korea, too. First broadcast in 2015, the popular coming-of-age drama “Answer Me 1988” revolves around five high-school pals in Northern Seoul, the basement where they hang out and the back alley where their moms shuck vegetables.

For once in K-drama, the headline here is not romance, but friends, family and the quiet intimacy of childhood. The young actors have an easygoing chemistry, and the writers and set designers deserve credit for their portrait of Korea in the ’80s, which includes realistic locations, references and slang. South Korean viewers responded enthusiastically to this attention to detail, with almost 20 percent of the population tuning in to watch the finale.

If You Like Dramatic Love Stories

A scene from “Descendants of the Sun.” KBS

‘Descendants of the Sun’

Where to stream: Netflix, Hulu

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“Descendants of the Sun” explores a less glamorous, more heartbreaking side of the South Korean military than the typical show about shootouts in the Demilitarized Zone. The show’s heroine is a young surgeon who falls for a boy-band-level-cute captain in the South Korean army. Their opposing views on life and death become irreconcilable, however (he kills; she saves), and when soldier and surgeon find themselves in Iraq, crisis after crisis brings them back together. But military life provides many obstacles to their budding relationship.

Nearly 40 percent of all Korean viewers tuned in to watch the finale of this intimate tale of love on the battlefield, and the show exposes a much deeper fault line in contemporary South Korean culture: the fierce militarism of the post-Korean War generation butting up against the waning nationalism of Korean millennials, whose ideals can tend toward mutual understanding and healing. The 16 episodes of Season 1 are available for American audiences to stream; a three-part special that aired in South Korea the week after the season finale is not currently available to stream in the United States.

If You Like Epics

Kim Go-eun, left, and Gong Yoo in “Goblin: The Great and Lonely God.” Hwa&Dam Pictures

‘Goblin: The Great and Lonely God’

Where to stream: DramaFever, Viki

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Korean myths of destiny, spirituality and reincarnation are interwoven in this epic tale of an immortal goblin’s quest to end his life. The goblin was once a handsome general, who provoked his young king’s jealousy with his exploits on the battlefield. Brutally executed by the king, he is sentenced by God to repay the lives that have perished at his sword. The king, meanwhile, is reincarnated as the grim reaper, allowing them to continue their rivalry as supernatural beings.

Trapped on mortal planes but unbound by time, the goblin (who looks mostly like a handsome young man), seeks a human bride, whose love will release him into the afterlife. When he is summoned by a luckless modern girl with a gift for seeing supernatural beings, he begins to think he has found something to live for. The show has an all-star cast, elaborate period costumes and moments of slapstick. If you like the time-traveling fantasy of “Outlander” or the demonic moments in “Buffy the Vampire Slayer,” this “cruel, romantic, sad love story” is for you.

If You Like Tales of Cross-Dressing and Class-Crossing

Yun Eun-hye, left, and Gong Yoo in “Coffee Prince.” MBC

‘Coffee Prince’

Where to stream: DramaFever, Viki

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K-dramas often offer redemption for the selfish young playboys of Seoul’s capitalist boom. In most cases, this comes by way of an unexpected romance with a hard-working young woman with a sassy lip, humble beginnings and a heart of gold. In “Coffee Prince,” there is also Shakespearean-style cross-dressing.

Han-kyul, the heir to a Seoul coffee dynasty, could make David Larrabee from “Sabrina” look industrious, but then his family orders him to run a successful coffee shop — or else. With a crew of handsome young male baristas as his marketing strategy, he turns an old restaurant into a hip cafe. One of the baristas, though, is actually a young woman, Eun-chan, who’s posing as a man to support her family. Love might transcend stereotypical gender presentation and income classes in South Korea, but there’s always the family to please.

If You Like Quirky Teen Dramas

Jung So-min, left, and Kim Hyun-joong in “Playful Kiss.” Group Eight

‘Playful Kiss’

Where to stream: Netflix, Hulu

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Getting into college in South Korea is no easy task, with teenagers preparing to take the annual national entrance exam from a very young age. “Playful Kiss” makes these pressures the backdrop to a quirky tale of teen romance, sprinkled with moments of magical realism.

The show centers on the spacey girl Hani, a high-school senior whose eye is more focused on the cruel, popular Seung-jo than on getting into college. Unfortunately, Seung-jo gets full marks in standardized tests and is looking for a girl who can match him. Soon, Seung-jo is helping her study, and their growing closeness piques the jealousy of Jungu, a rockabilly kid with an earnest crush on Hani. Like quite a few K-dramas, the show is based on a Japanese manga. It also has a comparatively straightforward plot, which may explain its only moderate success in South Korea. If you’re looking for a light and warm teen show, though, “Playful Kiss” is a charming watch.

If You Like Superhero Tales With a Twist

Park Bo-young in “Strong Girl Bong-Soon.” Drama House

‘Strong Girl Bong-Soon’

Where to stream: Netflix, Hulu

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If you’ve binged your way through all of the superhero series Marvel has to offer, behold “Strong Girl Bong-Soon.” Petite, unassuming Do Bong-soon has a Hulk-like strength passed down through the XX chromosomes of her family line. This superpower can only be used for good, so Bong-soon lives a carefully mortal, caustically boring life.

Of course, this can’t last for long. Once others learn of her gifts, she helps form a crime-fighting team to counter a wave of neighborhood kidnappings, helping Bong-soon find meaning in her formerly purposeless life. This delightfully nerdy tale with comic book influences combines the moral core of Batman with the humor of “Iron Man” and the love triangle of “X-Men.”

If You Like Your Ghost Stories Sexy

Jo Jung-suk, left, and Park Bo-young in “Oh My Ghost.” Chorokbaem Media

‘Oh My Ghost’

Where to stream: Netflix, DramaFever, Viki

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Korean TV’s orientation toward family values has garnered it popularity with broadcast channels in predominantly Muslim countries like Indonesia and the United Arab Emirates. In K-drama, sexual desire is depicted mostly indirectly, with characters awakening from delicious dreams and with almost-kisses interrupted by buzzing cellphones. In “Oh My Ghost,” the slant is slightly more supernatural.

Soon-ae haunts the earth as a lascivious ghost until she has sex for the first time. In desperation, she seizes the body of a meek assistant cook named Bong-sun. This plot device performs the function alcohol usually does in K-drama, allowing the shy Bong-sun to talk back to her handsome boss. The series morphs from a supernatural romance to a spooky thriller, a perfect distraction from your earthly troubles.

If You’re a Foodie

A scene from “Let’s Eat 1.” CJ E&M

‘Let’s Eat 1’

Where to stream: Netflix, DramaFever

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Soo-kyung is a divorced woman who wants nothing more than to slurp noodles all day in peace. In South Korea though, dining alone is a faux pas, so she’s on the hunt for the perfect dining partner. She may have found it in a verbose neighbor, Dae-young, whose poetic soliloquies venture into mansplaining. She’s starting to warm to his questionable charms when another neighbor, the winsome Jin-yi, comes on the scene. The three neighbors form an unlikely supper club.

As usual in K-drama, side plots abound, from a neighborhood crime story to unrequited workplace crushes. But it’s the food that keeps you bingeing. Close-ups of saucy black bean jjajangmyun noodles, crispy noorongi rice and buttery clamfests make “Let’s Eat 1” a visual feast — and will have you calling your local Korean restaurant for takeout.

If You Like Shows About Young Female Friendships

A scene from “Hello, My Twenties!” Celltrion Entertainment

‘Hello, My Twenties!’

Where to stream: Netflix, DramaFever

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In a similar vein to “Girls,” this show follows five young female roommates as they struggle to balance traditional expectations for women with the drive for self-fulfillment promised by capitalism — the difference being that, for South Koreans, traditional values include Confucian ideals of altruism and respect for one’s elders.

The show is pitched as a “slice-of-life” drama, but in true K-drama style there are also knockdown brawls over borrowed clothes and a side plot featuring the mysteriously lingering ghost of an ex-roommate. “Hello, My Twenties!” tackles some of the biggest issues faced by young women in South Korea: sex and relationships, alcoholism, body image and life outside the extended family.

If You Like High Concept Love Stories

A scene from “I’m Not a Robot.” May Queen Pictures

‘I’m Not a Robot’

Where to stream: DramaFever, Viki

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Finding companionship is hard, even when you’re not allergic to other human beings. For a certified genius named Min-kyu, skin-on-skin contact gives him rashes. To help, a scientist builds him a robot who looks just like a real woman. The robot malfunctions, and so the real woman it was modeled after ends up pretending to be the robot, and sparks fly (pun intended.)

The series can be read as commentary on the trend in which many young Koreans are waiting much later than their parents did to get married, if they get married at all. Included is a not-so-subtle message to millennials that it’s better to settle for a mate with a warm body than to search for cold perfection.

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And for a deeper dive into K-drama, check out:

“Weightlifting Fairy,” available on DramaFever and Viki.

“My Love From Another Star,” available on DramaFever and Viki.

“Winter Sonata,” available on Netflix and DramaFever.

“Gu Family Book,” available on DramaFever and Viki.

“All in,” available on DramaFever.

“Boys Over Flowers,” available on Netflix and Hulu.

“Autumn in My Heart,” available on DramaFever and Viki.