Effective field theories (EFTs) usefully exploit the simplicity that follows from a hierarchy of scales, and provide the framework that justifies controlled semiclassical calculations with gravity. Inflation raises two conceptual questions for EFTs: What controls EFTs when fields are larger than the Planck scale? and What is the EFT governing extra-Hubble physics during inflation? This talks provides answers to both questions. Pseudo-Goldstone bosons are used as examples of controlled large-field EFTs, with the message being that these can lead to more general potentials than the usual trigonometric ones. It is argued that the EFT describing extra-Hubble physics exists, but is not capturable in terms of an effective lagrangian. The proposed EFT explains why primordial quantum fluctuations quickly decohere while outside the Hubble scale, re-entering as classical fluctuations in the field eigen-basis. It also explains why fluctuation probabilities are described by Starobinsky's stochastic framework, and provides a first-principles derivation of it (plus, in principle, its leading sub-dominant corrections).