Pulsar timing arrays (PTAs) consist of a set of regularly monitored millisecond pulsars with extremely stable rotational periods. The arrival time of pulses can be altered by the passage of gravitational waves (GWs) between them and the Earth, thus serving as a galaxy-wide GW detector. Evidence for the first detection of low-frequency (~nHz) gravitational waves has recently been reported across multiple PTA collaborations, opening a new observational window into the Universe. Although the origin of the GW signal is yet to be determined, the dominant sources are expected to be inspiralling supermassive black holes. I will discuss a recent work in which we compare the GW detections by PTAs with the expected signal implied by existing electromagnetic observations in a simple but robust manner. We highlight that there is a simple upper limit to the GWB amplitude and that the currently measured GW amplitude is somewhat larger than expected. I will then show that additional information regarding the typical number of sources contributing to the background can already be inferred from current PTA data.