We will discuss quasi-de Sitter geometry of the inflationary universe and thermodynamics of its horizon. If one calculates the energy flux of the slowly rolling scalar field through the horizon, one finds that the first law of de Sitter thermodynamics dE=TdS reproduces the Friedmann equation for the scalar field. Inflaton quantum fluctuations generate scalar metric perturbations which wiggle the horizon area, but dE=TdS remains valid and compatible with the linearized Einstein equations for perturbations. In this picture holography does not put constrains on inflation. We discuss the global geometry of inflation and how quasi-de Sitter thermodynamics may converge with its stochastic description.