Cosmological inflation predicts the existence of a stochastic background of gravitational waves, whose features depend on the model of inflation under consideration. There exist well motivated frameworks predicting an enhancement of the primordial gravity wave spectrum at frequency scales testable with CMB or with gravitational wave experiments, with distinctive features as parity violation and non-Gaussianity. I will explain the properties of such scenarios, and their distinctive predictions for what respect the gravity wave power spectrum and bispectrum. I will then discuss how to quantitatively test these predictions with current and future experiments.