Gravitational waves allow a glance into the properties and dynamics of the very early Universe.I will discuss the state-of-the-art of predicting a stochastic background of gravitational waves produced by cosmological first-order phase transitions.I focus on recent developments in understanding the dynamics of the primordial fluid and how to connect simulation results to observations and model building.Finally, I discuss the possibility to interpret the recent anomalies in pulsar timing arrays with this kind of signal
