After reviewing the interest of gravitational-wave astronomy for cosmology, I will focus on a model that has recently received a lot of attention: primordial black holes as dark matter. I will present the current status of this scenario, as well as some observations pointing towards the possible existence of primordial black holes, with abundances comparable to the one of dark matter. These include the gravitational waves from massive black hole mergers recently detected by LIGO/VIRGO. Finding an evidence of even a single primordial black hole could have groundbreaking consequences for our understanding of the early Universe, and of High Energy physics.