The detection of gravitational waves from mergers of compact binaries in the first two runs of Advanced LIGO-Virgo have led to a plethora novel and exciting results in fundamental physics and cosmology. The binary coalescence process, sweeping the components through a range of frequencies at highly relativistic velocities, has enabled some of the first tests of general relativity in its highly dynamical and extremely strong field regime. With the recent detection of the binary neutron star merger and its coincident electromagnetic counterpart, a first "standard-siren" measurement of the Hubble constant has been made.

In this talk I will discuss some of the future prospects. In particular, I will talk about (i) a possible test of the black hole no-hair conjecture from the observation of ringdown gravitational-wave signals; and (ii) a "statistical" method of estimating cosmological parameters which will work also for gravitational-wave sources without transient electromagnetic counterparts.