Cosmological inflation predicts the existence of a stochastic background of gravitational waves (GW), whose features depend on the model of inflation under consideration. There exist well motivated frameworks leading to an enhancement of the primordial GW spectrum at frequency scales testable with GW experiments, with specific features as parity violation, anisotropies, and non-Gaussianity. I will explain the properties of such scenarios, and their distinctive predictions for what respect GW observables. I will then discuss perspectives for testing these predictions with future GW experiments.