The LHC will explore fundamental physics at a new energy frontier. A spectrum of new particles at the TeV scale is expected on two theoretical grounds: explaining dark matter and generating the electroweak scale. Understanding the properties of such particles can clarify the nature of dark matter, the origin of the weak scale, symmetries of nature, and the multiverse. These particles can be discovered by identifying collision events characteristic of new physics in LHC data. Their properties can be measured by characterizing such new physics events in terms of decay modes and basic kinematics. I will describe how this can be accomplished and exciting possibilities for what we may discover.