Yu was the last of the "three great filmmakers" of the 1950s and 1960s (the other two being Kim Ki-young and Shin Sang-ok). Yu was most famous for OBALTAN: THE AIMLESS BULLET, a neorealist film about the hard life of the downtrodden after the Korean War.
But for me, my favorite Yu film was EMPTY DREAM, a remake of Tetsuji Takeji's DAYDREAM. Yu was arrested for EMPTY DREAM, even though the actress Park Su-jeong did not really appear naked (good summary at the link above). Anyhow, I saw EMPTY DREAM at the Puchon Fantastic Film Festival in 2004, when they played it with a restored soundtrack. Very interesting, surreal film, and completely different than OBALTAN.
Yu's SCHOOL EXCURSION is pretty fun, too, and it used to be available on DVD (although I have not seen it in stores for ages... maybe the Yongsan black market still stocks it).
Sadly, I am no expert of Yu's films. I only met him briefly a couple of times, when he was obviously of fading health, and I never really talked to him at all. But I am happy that I did at least meet him (and Shin Sang-ok). You can read about Yu in the Korea Times. Darcy's page on Yu is here. And of course you can always read Wikipedia.
You can also briefly see Yu Hyun-mok in these old news videos from the 1960s, here, here, and here (that last one is from the 2nd Grand Bell Awards, back in 1963, with Yu winning Best Director for his film TO GIVE FREELY).
(Btw, I swiped that pic from Darcy's website. I hope that is okay).