Gravitational waves are unique messengers to explore the very early universe, probing energy ranges far beyond the reach of photon or even neutrino astronomy. The holy grail in this context is to detect imprints left by cosmic inflation, which would shed light on the microphysics of inflation as well as on the entire subsequent cosmological history. In the simplest model of inflation such signals are however beyond the reach of current and planned gravitational wave interferometers. After reviewing this standard picture, I will discuss how considering a pseudoscalar inflaton (an axion-like particle) can be a real game-changer, boosting the primordial gravitational wave signal into the range accessible by experiments such as eLISA and LIGO/VIRGO and simultaneously generating a spectrum of primordial black holes, which can contribute to dark matter
