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Because the inflationary mechanism is extremely sensitive to UV-physics, theconstruction of theoretically robust models of inflation provides a uniquewindow on Planck-scale physics. We review efforts to use an axion with a shiftsymmetry to ensure a prolonged slow-roll background evolution. The symmetrydictates which operators are allowed, and these in turn determine theobservational predictions of this class of models, which include observablegravitational waves (potentially chiral), oscillations in all primordialcorrelators, specific deviations from scale invariance and Gaussianity andprimordial black holes. We discuss the constraints on this class of models inlight of the recent Planck results and comment on future perspectives. Theshift symmetry is very useful in models of large-field inflation, whichtypically have monomial potentials, but it cannot explain why two or more termsin the potential are fine-tuned against each other, as needed for typicalmodels of small-field inflation. Therefore some additional symmetries orfine-tuning will be needed if forthcoming experiments will constrain thetensor-to-scalar ratio to be r < 0.01.

A review of Axion Inflation in the era of Planck