The 2012 discovery of the Higgs boson during Run I of the Large Hadron Collider was a triumph for particle physics, validating the theory of the weak force and completing the Standard Model framework. Yet, for all the Standard Model can explain, there is much we don’t know about the weak scale. Now operating at near design energy, the LHC is exploring deep questions made urgent by the Higgs discovery: Is there a dynamical mechanism or a new symmetry of nature that stabilizes the weak scale against large quantum corrections? Is the Higgs boson alone, or is it part of a larger family? Is the Higgs elementary, or composite? These questions are closely connected and are significant drivers of searches for new phenomena at the energy frontier. During the next phases of the LHC program, theory effort will focus on assessing the implications of results for models of new physics, and motivating and exploring novel signatures and measurement opportunities. I will review the properties of the Higgs boson, the problem of naturalness, the connections between the questions posed above, and a sample of ongoing phenomenological work to develop new LHC probes of physics beyond the Standard Model.
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