The precision study of the 125 GeV Higgs boson offers a new window into the search for new physics beyond the Standard Model. To confront the predictions of models with new interactions, the experimental program should be designed to achieve 1% precision over the full spectrum of Higgs boson couplings, with minimal model-dependence in the analysis and with tight control of systematic errors. In this contribution, we will explain how a precision Higgs program with these capabilities can be achieved at the proposed International Linear Collider. We will compare the capabilities of the ILC to those of the high-luminosity LHC and those of other $e^+ e^-$ Higgs factory proposals.