Chan-Wook Park is probably best known for Oldboy, which won the Grand Prix of the Jury at the 2003 Cannes Film Festival. His Sympathy for Mr. Vengeance (2002) and Lady Vengeance (2005) are also currently streaming on Netflix. These next two films are interesting ventures in to very different genres: romantic comedy and vampire horror.
I'm a Cyborg, but That's Okay (Chan-wook Park, Korea, 2006, 107 minutes)
Netflix: Placed in a psych ward for believing she's a robot, troubled Young-goon forsakes food and attempts instead to charge her body with electronic devices. As her health deteriorates, another eccentric patient tries to inspire her to start eating again. Netflix link.
Thirst (Chan-wook Park, Korea, 2009, 133 minutes)
Netflix: When the smoke clears from a failed experiment to find a cure for a fatal disease, a devout priest finds himself forever changed. Specifically, he's a vampire -- but that isn't the only thing that's different. Now he's also willing to commit adultery with the wife of his childhood friend, a sin he never would have considered before. Kang-ho Song, Ha-kyun Shin and Ok-bin Kim co-star in this horror offering from Korean director Chan-Wook Park. Netflix link.
Lee Chang-dong's Poetry was particularly successful on the international film festival circuit, winning the 2010 Screenplay Award at the Cannes Film Festival. Poetry currently has a 100% Tomatometer critical rating at Rotten Tomatoes.
Poetry (Chang-dong Lee, Korea, 2010, 139 minutes)
Netflix: A poetry-writing class inspires serenely self-possessed grandmother Mija (Jeong-hie Yun) to open her senses to her suburban surroundings, but in rushes an array of unsettling discoveries in this lyrical South Korean melodrama. Along with a diagnosis of Alzheimer's disease comes information that Mija's teenage grandson was party to a horrific incident, and it is left to Mija to compose order from the untidy emotional consequences. Netflix link.
Kim Ji-woon is also known for his 2008 cult action film The Good, the Bad, and the Weird, which is also streaming on Netflix. I Saw the Devil is not for all tastes, but you'll realize that when you read the synopsis.
I Saw the Devil (Ji-woon Kim, Korea, 2011, 142 minutes)
Netflix: From famed thriller director Ji-woon Kim comes this edgy thriller about secret agent Dae-hoon (Byung-hun Lee), who discovers how far over the edge he will go in order to seek revenge after his fiancée is brutally slain by psychopathic serial killer Kyung-chul (Min-sik Choi). With the police baffled by Kyung-chul's murders, Dae-hoon decides to capture the killer, but his own increasing violence makes him wonder who the monster really is. Netflix link.
Bong Joon-ho had an international breakthrough hit with The Host in 2006, and that film just became available again on Netflix Watch Instantly. His most recent film, Mother, currently has a 95% Tomatometer critical rating at Rotten Tomatoes.
Mother (Joon-ho Bong, Korea, 2009, 129 minutes)
Netflix: A murder rocks a South Korean town and suspicion quickly falls on a reclusive, mentally challenged -- and alibi-free -- young man (Bin Won). When an inept public defender botches the boy's case, his mother (Hye-ja Kim) sets out to prove her son's innocence. Acclaimed director Joon-ho Bong (Memories of Murder) explores the lengths a mother will go to protect her child in this atmospheric crime thriller. Netflix link.