Abstract: Recently, a new particle was discovered at the Large Hadron Collider that is broadly consistent with the long-sought Higgs boson, apparently validating our basic picture of elementary particle physics. The discovery has profound implications for Nature, but also sharpens a deep puzzle: What dynamics allows the Higgs boson to exist? The LHC is in a prime position to address this puzzle head-on, through an extensive program of searches for new phenomena. The enormous rate and complexity of energetic proton collisions make this a challenging endeavor, one that demands a strong interplay between theory and experiment. In the past several years, theorists have been developing new approaches to interpreting the ubiquitous collimated sprays of debris from these collisions, called "jets," unlocking search channels that were formerly thought to be impossible. These approaches are already bearing fruit at the LHC, and continue to grow in importance. I will provide an overview of the current situation, highlighting some promising avenues for the next discovery.