Abstract: In the past couple of decades, many exciting theoretical ideas, from low energy supersymmetry to compositeness, have been developed to understand the huge hierarchy between the scale of electroweak interaction and the scale of gravity, the Planck scale. All of those ideas imply the existence of new elementary particles close to the electroweak scale. The Large Hadron Collider (LHC) at CERN, scheduled to start operation in 2007, will probe the energy scale up to one order of magnitude beyond the electroweak scale and provide data to explore the mechanism of generating the electroweak scale. In this talk, after a brief survey of those theoretical ideas, I will turn to the question of how to test them at the LHC. In particular, using low energy supersymmetry as an example, I demonstrate the challenges in extracting information from the LHC data. Several crucial steps in resolving this so called LHC inverse problem will be identified.