Gravitational waves are one of the most remarkable predictions of the theory of General Relativity, and their recent direct observation provided us with an extremely powerful tool to study Nature.

After a brief introduction to the techniques employed to detect gravitational–wave signals and reconstruct their parameters, we will discuss predictions for the capabilities of the future generation of ground–based gravitational–wave interferometers, namely the Einstein Telescope and Cosmic Explorer.

We will summarize and compare state–of–the–art forecasts for the capabilities of current and future gravitational–wave detectors to observe compact binary coalescences. These have been obtained thanks to the GWFAST tool that we developed, which has been the basis for several studies within the Einstein Telescope Collaboration. We will focus both on general figures of merit and on parameter reconstruction at the population level.

We will then study more in–depth the possibilities offered by third–generation instruments on some specific aspects of their science case.