Black holes (BHs) cover a wide range of mass: from the stellar BH binaries detected with LIGO / Virgo to the massive BHs residing at the center of galaxies. Both these populations will be detectable in future by LISA at low-frequency. In this talk, I will provide a general overview of the current detections from LIGO / Virgo, describing the current state-of-the-art and I will highlight the potential of the LISA mission.

Among the sources which the Laser Interferometer Space Antenna (LISA) will observe are the signals from Massive Black Hole Binaries during their inspiral, merger and ring-down phases. To estimate physical parameters of these systems and their localisations, one has to perform some form of Bayesian Inference. The most common approach to do it is through defining a likelihood function and producing posterior samples with some form of sampling technique. The disadvantage of such sampling methods is that they are slow.

Gravitational waves have a periodic effect on the apparent positions of stars on the sky. This effect can be quantified and hence ultra-precise astrometric measurements (like the ones from Gaia) can provide a new method to search for gravitational signals.

The stochastic gravitational-wave background is a superposition of many astrophysical and cosmological sources, such as unresolved compact binaries, cosmic strings, and phase transitions in the early Universe. We highlight the importance of source separation in the case of a detection. By separating the individual sources, we can reveal remnants of early-universe processes. We use the data from the third LVK observing run to explore the parameter space of first-order phase transition models. We then investigate signs of parity violation in gravitational-wave data.