The question what drives primordial inflation is the longstanding question for inflationary cosmology. The discovery of the SM Higgs boson made it a concrete question, "is it possible for the SM Higgs to drive inflation?", and there arise several proposals of "Higgs Inflation" On the other hand, the recent result of BICEP2 experiment, r=0.2+0.07-0.05, gives a severe constraint on the inflation model building. Then, the simplest model of Higgs Inflation is strongly disfavored. However, it cannot disfavor all the proposals. I will explain the general model of Higgs Inflation in the context of the Horndeski's theory and its current status.