The discovery of the Higgs boson completes the Standard Model of particle physics, but its very existence leads to a deep question that may shed light on what lies beyond. Does the mass of the Higgs emerge from natural dynamics near the weak scale? Or instead, is the Higgs mass the consequence of an incredibly precise tuning of the parameters of an underlying theory? I will review the status of supersymmetry as a resolution to this naturalness problem given the emerging Higgs discovery and other increasingly constraining LHC results. I will show how considerations of naturalness lead to new directions in supersymmetric model and signature space. I will also discuss how the Higgs boson itself may serve as a portal to new physics through its interactions with dark matter or other new light states.