Abstract: Pulsar timing array detection of a gravitational wave background represents a milestone in the field of gravitational wave astronomy. However, the origin of such a signal is still a matter of intense debate: while supermassive black hole binaries formed as a result of galaxy mergers represent the most obvious candidate for the gravitational wave signal, many "new Physics" models can potentially explain at least part of the detected background. In this seminar I will review the current observational and theoretical status of the field, with particular emphasis on the science cases that are currently being explored by members of the SKAO Gravitational Wave Working Group. Moreover, I will discuss how radio observations with the SKAO can contribute to this broader context, and, in particular, I will focus on a possible background detection strategy that involves both pulsar timing array and cosmological observables.