Super massive black holes have been found in the centre of massive galaxies, which have also been observed to merge. Consequently, the central black holes should also form a binary and merge when their host galaxies collide. The galaxy merger rate can be calculated from astrophysical observables, such as the galaxy stellar mass function, pair fraction and merger time scale. Using galaxy - black hole relations it can be converted into a super massive black hole binary (SMBHB) merger rate, i.e. the population of SMBHBs in the Universe. Additionally, properties of individual SMBHBs, like their eccentricities and the densities of their stellar environment, also have an impact on the emission of gravitational waves (GWs). All the GWs emitted by the population of SMBHBs form a gravitational wave background (GWB), which is one of the prime targets for PTAs. Although, PTAs have not been able to detect such a background yet, stringent upper limits on the GWB have been produced. This thesis aims to investigate what we can learn from these upper limits as well as what could be learned from a detection.