And then there's . The science-fiction film about a train carrying the last remnants of humanity has enjoyed considerable critical kudos and general play internationally. Screened yesterday at Sarajevo, it has also featured at other film festivals including the Berlinale and was released in France, Italy, the US and many other territories where South Korean films don't usually play.

Directed by Bong Joon-ho, it's a mainly English-language work that sees Song holding his own in a strong ensemble cast that includes Chris Evans, John Hurt, Jamie Bell and Tilda Swinton. "Working with an international cast was a new experience for me. We got along fine, although it was hard to overcome the language barrier," Song says. "If it'd been any other person directing this project I would have turned it down. It's because I have a strong working relationship with Bong Joon-ho, and I trust him, that I decided to go abroad and shoot this film."

At home in South Korea, first-time director Yang Woo-seok's - which opened in Hong Kong on June 19 and is still playing - is the most successful of Song's recent works. The human rights drama, which received a rapturous response from viewers with more than 11 million tickets sold, dominated public conversation for a time after its release at the end of 2013. So it's ironic to hear the actor say he initially turned the role down.

"Given that it is a story depicting the early life of president Roh Moo-hyun, who passed away not long ago [in 2009], I questioned whether I could perform the role in a way that would do honour to his family and the many people who admired him. I didn't have the self-confidence [so] I turned it down," he says.

But the screenplay refused to leave him. "It's such a strong story. After thinking it over for a week, I called the producer and told him, 'I can't get this story out of my head. I may not be up to it, but I'd like to give it a try'," Song says.

The film provided several challenges. Song and director Yang decided not to attempt a highly detailed impersonation, but in its vocal qualities and physicality, Song's performance recalls the late president in various ways.

The film's climax also involves some intense court scenes where the protagonist confronts powerful government figures who have arrested and tortured a group of young students.

"I'm more successful fleshing out my performances on the set, in a spontaneous way," Song says. "About 50 per cent is prepared in advance, and 50 per cent is done on the day of shooting. But for these court scenes, for the first time ever, I spent five days on the set by myself before we shot them. I knew they had to be perfect."

Song suspected might make an impression, but he never imagined the overwhelming response from the audience. "It's not that you can't find this type of film in Hollywood or elsewhere," he says. "Films of this genre are common. But the Korean audience had a sore spot in their hearts that this film touched. They may have known about this story, but it hadn't yet been fully told."

Song is now in production on Lee Joon-ik's , which will be released domestically in early 2015. He plays Yeongjo, the well-respected 18th-century monarch who ordered the death of his violent and mentally unstable son, Crown Prince Sado. "As I get older, I find myself drawn to roles that test me as an actor. For , it's quite a difficult character to play. He's an elderly man, and the dialogue will take some effort to master."

A boom of sorts in historical films is under way in South Korean films and TV dramas. Recent film starred Hyun Bin as Sado's son, Jeongjo, who took the crown, while Han Suk-kyu will portray Yeongjo in the upcoming SBS drama Secret Door.

"Many period films coming out these days are stylish and dynamic," Song says. " by contrast focuses on character rather than spectacle. There's some danger that audiences might find it boring, but this film will offer well-developed characters and a strong focus on the performances. In that sense I'm feeling tremendous pressure," he says, laughing.

sees Song continuing to move away from stereotype. "People have this image of me as a somewhat common, bumbling character, like the guy around the corner. Of course, just because you suit a particular character well doesn't mean that your actual personality is similar," he says.

"Privately, I'm more withdrawn and sensitive than people might expect. But I do think that it's important to take on roles such as and that present a different image to the audience," the actor says.

As someone who has witnessed and taken part in the renaissance of South Korean cinema over the past decade and a half, Song identifies diverse content as the industry's current strength.

"I don't think the overall quality of South Korean films has improved compared to a decade ago, though obviously there have been some technical advances. But filmmakers have been able to explore a wide range of topics and subject matter," he says. "This seems to be one of the industry's greatest strengths. There has been a great effort on the part of many people to find new material and develop new stories."

But it's not an exaggeration to count Song among the industry's strong points. He has played a central role in so many recognised films that it's hard to imagine contemporary South Korean cinema without him. Years later, when people look back on this era, Song's expressive yet enigmatic face is likely to be one of its enduring images.