Open problems in Lie theory?

Hello, i'm a senior math major. I love mathematics, and I'm very interested in Lie algebras and groups, especially the exceptional groups. I took an independent study in Lie algebras last semester, and am continuing it this semester. Considering how recently( 2007 ) e8 was fully calculated out, I feel as if this is like a new frontier in mathematics, and we finally got the map. What is there to do though? I'm only just learning about these structures, so i'm not exactly up to date on the latest research.