The discovery of the Higgs boson at the Large Hadron Collider marks the culmination of a decades-long quest for the final piece of the Standard Model. But the discovery of the Higgs also adds new urgency to the hierarchy problem, namely the question of why the Higgs boson is so light despite its unique quantum sensitivity to much higher energy scales. This puzzle is made all the more challenging by the lack of evidence thus far for conventional approaches to the hierarchy problem at the LHC and other experiments. I'll discuss the essential features of the hierarchy problem and its possible solutions, with a particular focus on new approaches to the problem that have emerged in the years following the Higgs discovery. These new approaches feature novel experimental signatures, add urgency to the measurement of Higgs properties, and may shed light on dark matter and other mysteries of the Standard Model.