Seeking cracks in the Standard Model

In particle physics, it's our business to understand structure. I work on the Large Hadron Collider (LHC) and this machine lets us see and study the smallest structure of all; unimaginably tiny fundamental particles, held together by fundamental forces to provide the microscopic skeleton of matter.

The LHC is shut down at the moment, but will start gearing up for another round of data-taking in about six week's time. Given our success at teasing out the subatomic structure of the universe from the data we've already got, why do we need more? What unfinished business drives us to carry on?