In the coming years, LHC experiments will measure Higgs properties, such as its couplings, with increasing precision. Electron-positron Higgs factories, such as the ILC or TLEP, would be able to achieve even better precision. In this talk, I will discuss some of the physics questions that can be addressed by a precision Higgs coupling measurement program. First, the issue of naturalness of the electroweak scale can be addressed in a robust, model-independent manner. Second, the possibility of a first-order electroweak phase transition can be definitively probed, testing one of the necessary conditions of electroweak baryogenesis scenario.