Abstract: The discovery of the Higgs boson at the LHC marked the culmination of a decades-long quest for the final piece of the Standard Model. But the discovery of the Higgs also added 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 for conventional approaches to the hierarchy problem at the LHC and other experiments. In this talk I'll discuss the essential features of the hierarchy problem and its many possible solutions — ranging from the familiar to the highly speculative — with a particular focus on new developments connecting the hierarchy problem to gravity and cosmology.