From what I can tell from the chart, since Yu Ch'ang-hyeok played Yi Chae-ung this past Saturday, that was the quarter final, so the next few games should be interesting. The show appears to be televised 01:10-02:40 every Saturday night (Korean time). It might be cool to catch it live on 1TV.
The KBS cup uses a double elimination format. The next game (between Yoo Changhyuk and Lee Sedol) could be seen as a kind of quarter-final, but there are no other quarter-final matches, so it would be a rather strange way of looking at it. Basically, the winner faces Lee Chang-ho (who lost the winner's bracket final), and the winner of that faces Choi Ch'eol-han (who won the winner's bracket) in a best-of-3 final.
Full draw is available at http://igo-kisen.hp.infoseek.co.jp/kbs.html