After the discovery of Higgs particle at LHC, we can now say that the Standard Model of particle physics (SM) is completed. However, we cannot still explain the Universe with the SM as it is. In this talk, I will focus on inflation , which is now an (almost) indispensable ingredient in the modern cosmology, and explain the possible ways to drive inflation by the SM Higgs field itself. In particular, I will explain the self consistency of these scenarios and the relation to the electroweak vacuum stability. If time permitted, I will also talk about the electroweak vacuum stability during and after inflation in the case where inflation is driven by other sector than the SM.