Gravitational wave (GW) astronomy has came to revolutionize our understanding of astrophysics, cosmology and fundamental physics. GWs from binary black-hole (BH) mergers allow us to learn about the population of BHs, their origin and their role through the history of the universe. If these BHs have a primordial origin and are abundant enough, they could comprise a large fraction of the Dark Matter (DM). As a case of study, I will present the primordial black-hole production in Critical Higgs Inflation, a particle physics motivated model in which the SM Higgs is both responsible of inflation and DM, and discuss its GWs signatures. Moreover, GWs detected with an associated counterpart can probe the evolution of the universe and Dark Energy (DE). The recent measurement of the GW speed following GW170817 is an excellent example of the immense potential available to GWs tests of gravity. I will present the conditions for anomalous GW speed and classify the theories for DE that remain viable after GW170817. Finally, I will discuss how other propagation effects could also shed light on the quest for the nature of DE.